ECLECTIC    EDUCATIONAL    SERIES. 


THE 


ELEMENTS  OF  PHYSICS 


A  TEXT-BOOK   FOR 


ACADEMIES  AND  COMMON  SCHOOLS 


BY 


SIDNEY  A.  NORTON,  A.  M. 


WILSON,  HINKLE  &  CO. 

137   WALNUT  STREET  28   BOND    STREET 

CINCINNATI  ,NEW  YORK 


TO    PjU'AA 


COPYRIGHT,  1875,  BY  WILSON,  HINKLE  &  CO. 


ELECTROTVPED  AT 

FRANKLIN  TYPE  FOUNDRY, 

CINCINNATI. 


ECLECTIC  PRESS  : 

WILSON,  HINKLE  &  CO. 

CINCINNATI. 


PREFACE. 


This  volume  lias  been  prepared,  at  the  request  of  many 
teachers,  for  the  use  of  pupils  in  academies  and  common 
schools.  The  topics  considered  have  been  selected  with  ref- 
erence both  to  the  average  age  of  such  pupils  and  to  the 
time  usually  allotted  to  the  study  of  Physics. 

The  object  of  this  book  is  not  merely  to  give  a  system- 
atic and  symmetrical  epitome  of  the  Science,  but  so  to  pre- 
sent each  topic  that  the  pupil  shall  receive,  from  the  first, 
clear,  accurate,  and  scientific  ideas.  In  no  other  way  can 
the  study  of  any  science  be  made  a  means  of  mental  dis- 
cipline. No  pains  have  been  spared  to  attain  this  result; 
and  it  is  hoped  that,  however  much  has  been  omitted  that 
many  teachers  would  desire  to  have  presented,  the  pupil  will, 
at  least,  have  nothing  to  unlearn. 


869010 


TABLE   OF  CONTENTS. 


CHAPTER   I. 
GKKERAL  NOTIONS  OF  MATTER  AND  FORCE    . 


CHAPTER   II. 
PHENOMENA  CONNECTED  WITH  COHESION 27 

. 
CHAPTER   III. 

PHENOMENA  CONNECTED  WITH  ADHESION 33 

CHAPTER   IV. 
THE  LAWS  OP  MOTION 41 

CHAPTER  V. 
PHENOMENA  CONNECTED  WITH  GRAVITATION 50 

CHAPTER  VI. 

THE    LAWS    OP    FALLING   BODIES 5? 

CHAPTER  VII. 
THE  PENDULUM 65 


vi  CONTENTS. 

CHAPTER  VIII.  PAGX 

SIMPLE  MACHINES 72 

CHAPTER   IX. 
FLUIDS  AT  REST .        .91 

CHAPTER   X. 
FLUIDS  IN  MOTION 103 

CHAPTER  XI. 

THE    PHENOMENA    OP   AERIFORM    FLUIDS 108 

CHAPTER  XII.         , 

THE    MODES    OF    MOLECULAR    MOTION 128 

CHAPTER   XIII. 

ACOUSTICS,  OR   THE    PHENOMENA    OF   SOUND 135 

CHAPTER   XIV. 

OPTICS,  OR   THE    PHENOMENA    OF    LIGHT 153 

CHAPTER   XV. 

THE  PHENOMENA  OF  HEAT,  OR  PYRONOMICS 196 

CHAPTER    XVI. 
ELECTRICITY  .    228 


THE 


ELEMENTS  OF  PHYSIOS. 


CHAPTER  I. 

GENERAL  NOTIONS  OF  MATTER   AND   FORCE. 

1.  Matter  is  any  thing  that  is  capable  of  affecting  our 
senses.     The  objects  that  surround  us,  the  food  we  eat,  the 
water  we  drink,  the  air  we  breathe,  are  different  forms  of 
matter. 

2.  A  body  is  any  separate   portion  of  matter,  whether 
large  or  small:    thus  a  mountain,  a  pebble,  or  a  dew-drop, 
is  a  body.      The  different   materials  of  which   bodies  are 
composed  are  called  substances:    thus  iron,  wood,  and  sugar 
are  substances. 

3.  Some  substances  contain   but   one  kind  of  matter. 
These  are  called  simple  substances,  or  the  ELEMENTS.    There  are 
sixty-three  elements  now  known.     The   most  abundant  of 
these   are  oxygen,  silicon,   aluminium,  iron,  calcium,  mag- 
nesium, sodium,  potassium,  nitrogen,  hydrogen,  and  carbon. 

4.  Compound  substances  are  composed  of  at  least  two 
elements,  so  firmly  united  that  they  can  not  be  separated 
except  by  chemical  processes.      These  compound  substances 
make  up  the  bulk  of  the  globe :    thus  water  is  composed  of 

(7) 


8  ELEMENTS  OF  PHYSICS. 

oxygen  and  hydrogen ;  quartz  and  white  sand,  of  silicon  and 
oxygen;  clay,  mainly  of  silicon,  oxygen,  and  aluminium. 

*  X  ,5.  Many^odies  are  mixtures  of  several  substances:  thus 

,  gunpowder  is  a  mixture  of  niter,  carbon,  and  sulphur.      The 

^ahvfe  al&o "a  mixture.     The  most  important  of  its  constituents 

are  oxygen,  nitrogen,  carbonic  acid,  and  the  vapor  of  water. 

6.  Many  substances  can  exist  at  different  times  in  three 
different  states:  thus  water  can  exist  as  ice,  as  water,  or  as 
steam. 

A  body  is  in  the  solid  state  when  its  particles  are  held  firmly 
together,  and  retain  the  shape  that  has  been  given  them  by 
nature  or  art.  Ice,  wood,  and  tallow  are  solids. 

A  body  is  in  the  liquid  state  when  its  particles  easily  change 
their  relative  positions.  When  a  liquid  is  poured  into  an 
open  vessel,  it  adapts  itself  to  the  shape  of  the  vessel,  except 
that  its  upper  surface  is  horizontal.  Water,  alcohol,  and  oil 
are  liquids. 

A  body  is  in  the  aeriform  state  when  its  particles  tend  to 
separate  from  each  other,  and  to  occupy  a  greater  volume. 
Bodies  in  this  state  are  called  aeriform  bodies,  gases,  or  vapors. 
Aeriform  bodies  can  not  be  retained  in  an  open  vessel ;  and 
when  shut  in  on  all  sides,  completely  fill  the  vessel  in  which 
they  are  placed.  Steam,  the  air,  and  illuminating  gas  are 
aeriform  bodies. 

The  term  fluid  is  applied  both  to  liquids  and  aeriform 
bodies :  thus  we  may  speak  of  water  as  a  liquid  or  as  a  fluid; 
or  of  air  as  an  aeriform  body  or  as  fluid. 

7.  No  one  can  conceive  of  a  body  which  does  not  possess 
length,  breadth,  and  thickness.  Even  the  fine  particles  of 
dust  which  are  seen  only  in  the  path  of  the  sunbeam  must 
have  a  certain  shape  or  figure,  and  occupy  a  certain  amount 
of  space.  The  amount  of  space  that  a  body  occupies  is 
called  its  bulk  or  volume. 


MEASURES. 


9 


The  ordinary  measures  in  the  United  States  are  derived 
from  an  arbitrary  unit  called  the  yard ;  although  we  may  use 
any  one  of  its  divisions  or  multiples  as  a  unit — as  the  inch,  foot, 
or  mile.  The  square  inch,  square  yard,  etc.,  are  units  of  sur- 
face. The  cubic  inch,  cubic  foot,  etc.,  are  units  of  volume. 

The  wine  gallon  of  the  United  States  contains  231  cubic 
inches.  The  imperial  gallon  of  England  contains  277.274 
cubic  inches. 

The  French  unit  of  length  is  the  metre, 
which  is  equal  to  39.3685  of  our  inches. 
All  the  French  measures  increase  or  de- 
crease in  decimal  proportion.  For  the 
increase  the  Greek  prefixes  deca  (10), 
hecto  (100),  and  kilo  (1000),  are  used; 
for  the  decrease  the  Latin  prefixes  deci 
(TL),  centi  (y^j-),  and  milli  (^Vir)'  are 
used.  A  decimetre  is  drawn  in  Figure  1, 
in  comparison  with  a  scale  of  inches. 
One  inch  is  very  nearly  25.4  millimetres. 

The  French  unit  of  volume  is  a  cubic 
decimetre,  and  is  called  the  litre.  It 
contains  61.022  cubic  inches,  or  2.113 
wine  pints. 

8.  All  bodies  may  be  divided  into 
very  minute  particles:  thus  stones  may 
be  crushed  to  powder;  the  hardest  steel 
may  be  broken;  and  even  the  diamond 
may  be  reduced  to  dust.  Wonderful  ex- 
amples of  minute  divisibility  are  afforded 
by  odors  and  coloring  matters.  Odors 
can  be  caused  only  by  particles  of  matter  FIG.  i. 

in  the  air;    and  yet  how  small  must  those  be  that  enable 
a  hound  to  follow  his  game !    A  grain  of  musk  has  perfumed 


10  ELEMENTS  OF  PHYSICS. 

a  large  apartment  for  several  years  without  perceptibly  los- 
ing in  Aveight.  An  ounce  of  aniline  is  capable  of  coloring 
two  hundred  ounces  of  silk  thread.  We  may  separate  this 
thread  into  3,000,000,000,000  parts  and  discern  the  red  color 
of  the  aniline  in  each  one  of  them. 

Many  chemical  tests  reveal  the  presence  of  exceedingly 
small  quantities  of  matter.  If  a  grain  of  iron  or  of  copper 
be  dissolved  in  nitric  acid,  and  then  added  to  a  tumblerful 
of  water,  the  presence  of  either  metal  may  be  detected  in 
every  part  of  the  mixture.  This  may  be  done  by  placing  a 
drop  of  the  solution  on  a  watch-glass  and  then  adding  a  solu- 
tion of  ferrocyanide  of  potassium,  when  the  iron  solution  will 
be  turned  blue,  and  the  copper  solution  will  be  reddened. 

Even  by  mechanical  means  we  may  obtain  particles  so 
small  that  it  is  difficult  to  form  just  conceptions  of  their 
size.  Gold  leaf  is  sometimes  so  thin  that  fifteen  hundred 
leaves  placed  one  above  another  will  not  equal  the  thickness 
of  ordinary  paper.  One  square  inch  of  this  leaf  weighs  less 
than  one  twenty-thousandth  part  of  an  ounce ;  and  we  can 
divide  this  into  ten-thousand  parts,  each  one  of  which  is 
distinctly  visible  to  the  eye,  though  weighing  less  than  one 
two-hundred-millionth  part  of  an  ounce. 

9.  There  are  many  reasons  for  believing  that  there  is 
a  limit  to  the  divisibility  of  matter.     The  smallest  eonceiv- 
able  particle  of  water,  or  of  any  compound  body,  is  called  a 
molecule.     A  molecule  is  so  small  that  no  microscope  -will 
ever  enable  us  to  see  it.     It  is  the  smallest  particle  into 
which  a  body  may  be  divided  without  losing  its  identity. 

10.  By  chemical  means  a  molecule  of  water  may  be  still 
further  divided  into  its  components  oxygen  and  hydrogen, 
and  thus  particles  obtained  which  are  the  smallest  conceiv- 
able.     These  are  called  atoms.      An  atom  is  the  smallest 
particle  of  matter  capable  of  entering  into  a  molecule. 


POROSITY.  11 

11.  How  the  atoms  are  arranged  to  form  molecules,  or 
how  the  molecules  are  arranged  in  bodies,  is  unknown.     We 
know  that  all  bodies  expand  when  heated,  and  contract  when 
cooled. #     Thus,  if  an  empty  flask  is  inverted  in  a  vessel  of 
water,  and  heat  is  applied  (Fig.  2),  the  air  will  expand  so 
much  that  a  portion  will  be  expelled. 

On  cooling,  the  air  remaining  in  the 
flask  will  resume  its  original  volume. 
We  know  also  that  all  bodies  are  made 
smaller  by  pressure :  thus  a  bottle  of 
' '  soda  water "  contains  several  times 
its  volume  of  compressed  gas,  which 
expands  to  its  original  volume  when 
the  cork  is  removed.  All  bodies  are 
expansible  and  compressible.  Gases  FIG.  2. 

show  these  properties  very  readily,  but  they  are  also  exhi- 
bited by  solids  and  liquids. 

These  and  similar  phenomena  render  it  probable  (1)  that 
the  molecules  of  a  body  do  not  touch  each  other,  but  are  sep- 
arated by  vacant  spaces  or  pores ;  and  (2)  that  the  molecules 
are  free  to  move  even  in  the  most  rigid  bodies.  When  bodies 
expand,  the  molecules  separate,  and  the  pores  become  larger ; 
when  bodies  contract,  the  molecules  approach,  and  the  pores 
become  smaller. 

12.  The  pores  of  bodies  are  of  two  kinds.     (1)  Those 
which  exist  between  molecules  are  called  physical  pores.  These 
are  so  small  that  they  can  not  be  seen  even  by  the  aid.  of  a 
microscope.     (2)  Sensible  pores  are  cavities  that  may  be  seen, 
as  the  pores  in  bread,  or  in  some  kinds  of  wood. 

If  water  is  heated  in  a  glass  vessel,  bubbles  of  air  sep- 


*When  clay  is  heated,  it  contracts  permanently,  because  its  par- 
ticles suffer  a  chemical  change. 


12  ELEMENTS  OF  PHYSICS. 

arate  out  and  cling  for  a  time  to  the  sides  of  the  vessel. 
These  must  have  come  from  the  physical  pores  of  the  water. 
So  also,  if  a  cup  be  filled  to  the  brim  with  hot  water,  two 
or  three  spoonfuls  of  pulverized  sugar  may  be  gradually 
added  before  the  cup  overflows.  The  molecules  of  the  sugar 
find  sufficient  space  in  the  pores  of  the  water.  Sometimes 
an  actual  contraction  of  volume  occurs  on  mixing  two 
liquids.  Thus,  if  a  long  and  slender  test-tube  be  half  filled 
with  water,  and  strong  alcohol  be  poured  carefully  in,  so  as 
not  to  mix  the  two  liquids  until  the  tube  is  quite  filled,  and 
then  the  tube  be  tightly  closed  and  inverted,  the  liquids  will 
mix  and  no  longer  fill  the  tube.  The  explanation  of  this 
phenomenon  is  that  the  molecules  of  the  alcohol  and  the 
water  are  mutually  so  arranged  as  partially  to  fill  the  pores 
previously  existing  in  the  two  bodies. 

13.  We  do  not  believe  it  possible  that  any  two  particles 
of  matter  can  occupy  the  same  place  at  the  same  time.  In 
other  words,  we  believe  that  matter  is  impenetrable.  If  a 
pebble  be  dropped  into  a  tumblerful  of  water,  enough  water 
will  overflow  to  equal  the  bulk  of  the  pebble.  The  ex- 
amples given  in  the  preceding  section  are  only  apparent 
exceptions  to  the  property  of  impenetrability.  There  are 
other  apparent  exceptions,  which  can  be  even  more  readily 
explained. 

If  one  end  of  a  glass  tube  be  closed  by  the  thumb,  and 
the  other  end  plunged  into  a  vessel  of  water,  the  water  can 
not  fill  the  tube  because  of  the  impenetrability  of  the  air 
inclosed  in  the  tube.  Nevertheless  it  will  be  seen  that  the 
water  will  rise  a  little  way  in  the  tube;  but  this  is  because 
the  air  is  compressed,  and  so  allows  space  for  the  water  to 
enter. 

An  easy  experiment,  which  illustrates  the  same  fact,  may 
be  made  by  wrapping  moistened  paper  around  the  tube  of  a 


DENSITY.  13 

funnel,  so  that  it  may  be  made  to  fit  air-tight  in  the  neck 
of  a  bottle,  as  shown  in  Fig.  3.    Now,  if  water  be 
quickly  poured  into  the  funnel,  only  so  much  will 
enter  the  bottle  as  corresponds  to  the  compressed  or 
displaced  air. 

14.  Space  which  contains  no  matter  is  called  a 
vacuum. 

15.  Bodies  vary  greatly  with   respect  to  the 
pores   which    they    contain.      Those    that    contain    FlG-  3- 
large  pores  are   called  rare  bodies ;    those   that  have  small 
pores  are  called  dense  bodies.     Density  is,  therefore,  a  term 
which  expresses  the  relative  amount  of  matter  which  equal 
volumes  of  different  substances  contain.     Iron,  for  example, 
is  denser  than  stone,  but  is  less  dense  than  gold.     In  com- 
paring the  relative  density  of  bodies,   it  is  convenient   to 
select  some  substance  which  shall  be  taken  as  the  standard 
of  comparison,  and  reckoned  as  unity,  or  1.     Thus  the  air 
is  a  standard  of  density  for  all  aeriform  bodies,  and  water  is 
a  standard  of  density  for  liquids  and  solids.     It  is  also  nec- 
essary to  select  some  temperature  at  which  the  comparison 
shall  be  made.    The  temperature  usually  taken  is  32°  F.  for 
all  bodies  excepting  water,  which  is  unity  when  at  39°. 2  F. 
In  the  case  of  gases,  it  is  also  necessary  that  they  should  be 
compared  when  under  the  same  pressure.     The  pressure  as- 
sumed is  the  average  pressure  of  the  atmosphere  at  the  level 
of  the  sea,  which  is  14.7  pounds  to  the  square  inch,  and 
which    equals   a   column  of  mercury   29.92    inches    high.* 
These  are  called  the  normal  conditions  of  temperature  and 
pressure. 

16.  The  ratio  which  shows  how  many  times  heavier  any 
given  substance  is  than  an  equal  volume  of  water  or  of  air, 


*Sec  Section  31. 


14  ELEMENTS  OF  PHYSICS. 

under  the  normal  conditions,  is  the  specific  gravity  of  the  sub- 
stance. The  specific  gravity  of  chlorine  gas  is  2.47,  which 
means  that  a  given  bulk  of  chlorine,  as  a  pint  or  a  gallon,  is 
2.47  times  heavier  than  the  same  bulk  of  air.  The  specific 
gravity  of  silver  is  10.5,  which  means  that  a  given  bulk  of 
silver,  as  a  cubic  inch,  weighs  10.5  times  more  than  the  same 
bulk  of  water. 

Weights  of  the  Standards. 

One  cubic  inch  of  air  weighs,  at  32°  F.,  0.32712  grains. 

at  60°  F.,  0.30954  grains. 

One  cubic  in.  of  water  weighs,  at  32°  F.,  252.875      grains. 

at  60°  F.,  252.456      grains. 

Specific  Gravities  Compared. 

at  32°  F.  at  62°  F. 

Katio  of  air  to  water,     1  to   773.2          1  to  816.8 
Ratio  of  water  to  air,     1  to  .00129363  1  to  .0012243 

Table  of  Specific  Gravities. 


Air, 

1. 

Cork, 

0.24 

Steam, 

.622 

Ice, 

0.93 

Hydrogen, 

.069 

White  Oak, 

0.86 

Oxygen, 

1.106 

Ebony, 

1.33 

LIQUIDS. 

Glass, 

3. 

Pure  Water, 

1. 

Iron, 

7.78 

Sea  Water, 

1.026 

Copper, 

8.85 

Olive  Oil, 

0.915 

Lead, 

11.35 

Sulphuric  Acid,     1.84  Gold,  19.26 

Saturated  Brine,    1.205  Platinum,         21.53 

17.  Matter  is  every- where  subject  to  change.  When 
the  smith  heats  a  bar  of  steel,  it  expands ;  when  he  beats  it 
on  his  anvil,  he  is  changing  its  form;  when  he  hurls  it  from 


MOTION.  15 

him,  he  is  changing  its  position.  If  the  steel  be  rubbed  on 
a  magnet,  it  acquires  the  property  of  attracting  iron  filings. 
It  may  be  melted  to  a  fluid  state  and  cast  into  any  shape. 
Such  changes  as  these  are  called  physical  changes.  Physical 
changes  are  those  by  which  the  substance  is  not  altered  so 
as  to  lose  its  identity. 

On  the  other  hand,  in  chemical  changes  the  identity  of  the 
substance  is  entirely  lost.  Thus,  when  steel  rusts,  the  red 
powder  which  forms  is  due  to  a  chemical  change  in  which 
water  has  been  decomposed  into  oxygen  and  hydrogen ;  the 
oxygen  has  united  with  the  iron  in  the  steel,  to  form  a  new 
kind  of  substance,  and  the  hydrogen  has  escaped  into  the 
air.  So,  also,  the  decay  of  leaves,  the  burning  of  wood,  the 
souring  of  cider,  are  chemical  changes. 

18.  Force  is  that  which  causes  any  change  in  the  form 
or  condition  of  matter.     All  the  phenomena  of  the  visible 
universe  are  caused  by  the  action  of  force  upon  matter. 

The  simplest  change  in  matter  is  that  of  position.  We 
determine  the  motion  or  rest  of  a  body  by  its  relation  to 
some  given  point ;  but  as  this  point  may  be  itself  fixed  or 
moving,  motion  or  rest  is  either  (1)  absolute,  or  (2)  relative. 

19.  Absolute  motion  is  change  of  place  with  regard  to  a 
fixed  point :   relative  motion  is  change  of  place  with  regard 
to  a  point  in  motion. 

The  motion  of  the  heavenly  bodies  with  reference  to  ideal 
fixed  points  in  space  are  examples  of  absolute  motion. 
Strictly  speaking,  no  bodies  are  in  a  state  of  absolute  rest. 
Every  particle  on  the  earth's  surface  partakes  of  all  the  daily 
and  annual  motions  of  the  earth;  and,  therefore,  the  terms 
absolute  motion  and  rest,  when  applied  to  bodies  on  the 
earth's  surface,  have  reference  to  objects  that  appear  fixed. 

A  person  seated  on  a  steamboat  in  motion  is  in  absolute 
motion  with  respect  to  the  harbor  he  has  left,  or  to  the  har- 


16  ELEMENTS  OF  PHYSICS. 

bor  he  is  approaching,  and  is  in  a  state  of  relative  rest  with 
regard  to  the  parts  of  the  vessel.  If  he  walks  toward  the 
stern  of  the  boat  as  fast  as  the  vessel  moves  forward,  he  is 
in  a  state  of  relative  motion  with  regard  to  the  parts  of  the 
vessel,  but  is  in  absolute  rest  with  regard  to  the  harbors. 

20.  Velocity  is  the  rate  of  motion.     It  may  be  found  by 
dividing  the  space  passed  over  by  the  time  occupied  in  the 
transit.     Thus,  if  a  locomotive  is  five  hours  in  going  one 
hundred  miles,  its  velocity  is  twenty  miles  an  hour. 

The  formula,  v  =  s  -f- 1 
Expresses  the  relation  between  space,  time,  and  velocity. 

21.  A  natural  unit  of  time  is  the  day,  but  any  of  its 
subdivisions — hour,  minute,  or  second — may  be  assumed  as 
convenience  dictates. 

Table  of  Velocities. 

MILES  PER  HOUR.  FEET  PER  SECOND. 

Man  walking,  3                           4.4 

Man  running,  10                          14.66 

Swift  trotting  horse,  27                          40. 

A  rifle  ball,  1,000  1,466.66 

Sound,  762  1,117.6 

22.  Motion  and   rest   are   equally  natural   to  a  body. 
When  the  forces  that  are  acting  upon  matter  exactly  balance 
each  other,  it  is  at  rest,  and  is  in  motion  when  they  do  not. 
We  say,  then,  that  matter  has  the  property  of  inertia,  by 
which  we   mean  that   it  tends   to   retain  its  present  state, 
whether  of  motion  or  of  rest. 

It  requires  some  force  to  set  a  body  in  motion,  and  when 
it  is  in  motion,  it  requires  force  to  stop  it.  The  inertia  of 
the  air  becomes  manifest  by  the  resistance  it  offers  to  a  body 
moving  through  it.  If  we  endeavor  to  run  with  an  open 
umbrella,  we  need  to  employ  considerable  force  to  overcome 


FORCES  IN  NATURE.  17 

the  resistance  of  the  air,  because  we  shall  have  to  displace 
or  set  in  motion  the  air  which  is  in  front  of  us. 

The  heavier  a  body  is,  the  greater  will  be  its  inertia ;  that 
is,  it  will  require  more  force  than  a  lighter  body  to  set  it  in 
motion,  or  to  stop  it  when  it  is  moving.  Thus,  a  small  boy 
will  easily  "dodge"  a  larger,  because  the  heavier  boy  will  be 
unable  to  -change  his  course  at  once. 

A  person  standing  in  a  wagon  partakes  of  its  condition  of 
motion  or  rest.  If  it  is  suddenly  set  in  motion,  he  is  thrown 
backward,  because  his  feet  are  drawn  along  by  the  friction 
against  the  bottom,  before  his  head  can  acquire  the  motion, 
forward.  If  the  wagon  is  suddenly  stopped  when  in  rapid 
motion,  he  is  thrown  forward. 

23.  There  are  many  forces  in  Nature,  and  it  is  conven- 
ient to  divide  them  into  three  classes. 

(1)  Those  which  act  only  upon  the  molecules  of  matter, 
and  at  distances  which  are  inappreciable  to  our  senses.   These 
are  named  Cohesion,  Adhesion,  and  Affinity.    Taken  collect- 
ively, they  are  called  the  molecular  forces. 

(2)  Those  which  act  also  upon  bodies  taken  as  a  whole, 
and   at   both  sensible   and   insensible  distances.     These  are 
Gravitation,  Light,  Heat,  and  Electricity. 

(3)  Those  which  take   part  in  the  phenomena  of  living 
plants  and  animals  by  controlling  or  modifying  the  forces  of 
inanimate  nature.     These  are  called  the  vital  forces. 

24.  Cohesion  causes  like  molecules  to  unite  in  one  mass. 
It  keeps  the  particles  of  a  body  together.     It  is  strongly  ex- 
erted in  solids,  feebly  in  liquids,  and  not  at  all  in  aeriform 
bodies.     Thus  a  dew-drop  is  spheroidal  because  of  the  co- 
hesive force.     When  the  drop  is  very  large  it  becomes  flat- 
tened, because  the  force  of  cohesion  is  partly  overcome  by 
the  force  of  gravitation. 

The  following  pretty  experiment  illustrates  the  tendency 

PHYS.  2. 


18  ELEMENTS  OF  PHYSICS. 

of  liquids  to  assume  the  spheroidal  form :  Take  a  wine-glass 
half  full  of  water,  and  carefully  fill  it  with  alcohol  so  as  not 
to  mix  the  two  liquids ;  then  drop  a  very  little  olive  oil 
through  the  alcohol.  It  will  come  to  rest  in  the  middle  of 
the  glass,  and,  if  the  quantity  taken  is  not  too  great,  will  as- 
sume the  shape  of  a  ball. 

When  the  cohesion  of  solids  has  been  once  destroyed,  it  is 
difficult  to  cause  the  particles  to  reunite.  If  a  bar  of  lead 
be  cut  in  two,  the  several  parts  may  be  made  to  cohere  by 
so  cutting  their  faces  that  they  will  present  a  bright  and 
even  surface,  and  then  pressing  them  tightly  together  with 
a  slight  twisting  motion.  Two  plates  of  polished  glass  will 
cohere,  under  pressure,  so  firmly  that  they  may  be  worked  as 
a  single  piece. 

25.  Adhesion  causes  the  molecules  of  different  kinds  of 
matter  to  cling  together.     Thus,  adhesion  causes  the  dust  to 
cling  to  any  thing  it  falls  upon ;    chalk  to  cling  to  black- 
boards, and  dew-drops  to  leaves.    Under  the  name  of  Friction 
it  diminishes  the  work  of  moving  force,  (1)  by  stiffening  the 
joints  of  machines,  (2)  by  increasing  the  resistance  to  be 
overcome.     Friction  often  acts  as  a  mechanical  advantage,  as 
in  retaining  nails  and  screws  in  their  sockets,  in  preventing 
our  feet  from  slipping  when  -  standing  or  walking,  and  in  en- 
abling us  to  take  firm  hold  upon  objects. 

26.  Affinity   causes   the   atoms   of  unlike   substances   to 
unite  and   form  new  kinds  of  matter.     All  chemical   phe- 
nomena are  due  to  affinity.     When  iron  dissolves  in  nitric 
acid  a  new  kind  of  matter   (the  nitrate  of  iron),  differing 
both  from  the  iron  and  the  acid,  is  formed. 

Adhesion  and  cohesion  differ  from  affinity  in  this,  that 
their  action  on  bodies  does  not  effect  any  essential  change  in 
the  properties  of  the  bodies  acted  upon.  They  differ  from 
each  other  in  this,  that  adhesion  acts  between  unlike  par- 


GRAVITATION.  19 

tides,  and  cohesion  between  like  particles.  They  all  agree  in 
this,  that  their  energy  increases  with  the  number  of  mole- 
cules that  are  acted  upon.  This  statement,  when  applied  to 
solids,  may  be  expressed  in  these  words :  the  energy  of 
molecular  forces  increases  with  the  extent  of  surface  exposed 
to  their  action. 

27.  Gravitation  is  a  force  by  virtue  of  which  every  par- 
ticle of  matter  attracts  every  other  particle  of  matter  toward 
itself.    The  term  mass  is  used  to- denote  the  amount  of  matter 
in  a  body,  and  it  has  been  established  that  gravity  is  propor- 
tional to  mass. 

If  a  stone  were  dropped  from  a  balloon  it  would  fall  to- 
ward the  earth  by  reason  of  the  attraction  of  the  earth,  or 
terrestrial  gravitation.  The  earth  also  tends  to  fall  toward 
the  stone,  but  its  mass  is  so  much  the  greater  that  its  motion 
is  inconceivably  small. 

But  gravitation  does  not  always  produce  motion.  A  stone 
resting  on  the  top  of  a  table  is  not  free  to  fall,  and,  in  such 
a  case,  the  force  of  the  earth's  attraction  is  expended  in 
pressure  against  its  support.  This  pressure  is  called  the  ab- 
solute weight  of  the  body.  Hence,  weight  is  the  measure  of 
the  earth's  attraction. 

28.  Gravity  is  also  influenced  by  distance,   as  will   be 
shown  hereafter.      An  iron  ball  which  weighs  one  hundred 
and  ninety-four  pounds  at  the  equator  will  weigh  one  hundred 
and  ninety-five  pounds  at  the  poles.     Hence,  weight  does 
not  always  mean  the  same  as  mass,  for  a  body  will  always 
contain  the  same  amount  of  matter  in  every  conceivable 
place.      Nevertheless,  as  weight  is   always   proportional  to 
mass,  we  may  use  weight  as  a  means  of  estimating  mass,  or, 
in  most  instances,  use  the  two  terms  interchangeably  without 
sensible  error. 


20 


ELEMENTS  OF  PHYSICS. 


29.  Universal  gravitation  is  the  same  force  applied  to 
the  heavenly  bodies.     It  is  by  reason  of  this  force  that  the 
earth  and  other  planets  move  round  the  sun. 

30.  The  unit  of  weight  adopted  by  the  United  States 
and  England  is  the  avoirdupois  pound  of  7,000  grains. 

The  French  unit,  called  a  gramme,  is  the  weight  of  a 
cubic  centimetre  of  distilled  water,  at  39°. 2  F.  A  gramme 
equals  15.434  grains;  a  kilogramme  equals  15434  grains,  or 
2.2046  avoirdupois  pounds. 

Weight  in  pounds  of  one  cubic  foot  at  62°  F. 


Air,  .  0.080728 

Water,  62.418 

Mercury,  848.75 

Potassium,  53. 


Wrought  Iron,     480. 
Copper,  556. 

Lead,  712. 

Gold,  1224. 

Gravitation  is  made  serviceable  to  man  in  the  force  of 
running  water,  and  in  machinery  moved  by  weights,  as  well 
as  in  giving  stability  to  buildings  and 
other  structures. 

31.  The  unit  of  pressure  in  most 
frequent  use  is  the  pressure  of  one  at- 
mosphere. This  pressure  is  due  to  the 
attraction  of  gravitation.  We  may 
ascertain  its  amount  by  the  experiment 
of  Torricelli. 

Fill  a  glass  tube,  thirty-two  inches 
long,  with  mercury,  close  the  open  end 
firmly  with  the  finger,  and  then  invert 
it  in  a  cistern  of  mercury,  Fig.  4.  On 
removing  the  finger,  the  mercury  will 
fall  a  little  way  in  the  tube  and  leave 
a  •  vacuum  above  it.  Now,  as  the  FlG-  4- 

weight  of  the  mercury  tends  to  make  it  flow  out  of  the 


EXPANSION  BY  HEAT. 


21 


tube,  the  column  must  be  sustained  by  an  equal  and  oppo- 
site force.  This  force  can  be  nothing  else  than  the  pressure 
of  the  atmosphere;  and,  hence,  this  pressure  may  be  meas- 
ured by  the  mercurial  column.  This  apparatus  is  called  a 
Barometer,  and  is  used  to  measure  the  pressure  of  the  air. 
At  the  level  of  the  sea,  and  at  32°  F.,  the  average  height 
of  the  mercurial  column  is  29.922  inches,  or  760  millimetres. 
A  column  of  this  height,  a  square  inch  in  section,  weighs 
14.73  pounds. 

We  are  accustomed  to  say  that  the  pressure  of  the  at- 
mosphere is  nearly  fifteen  pounds  to  every  square  inch  of 
surface. 

Table  of  Pressures. 


POUNDS  ON  THE 
SQUARE  FOOT. 


POUNDS  ON  THE 
SQUARE  INCH. 


One  atmosphere,  2121.12  14.73 

One  foot  of  water,  at  39°.2  R,         62.425  0.4335 

One  inch  of  mercury,  at  32°  F.,       70.73  0.4912 

32.  Heat  tends  to  make  the  molecules  of  matter  re- 
cede from  each  other.  When  a  body  is  warmed,  it  becomes 
larger;  when  it  is  cooled,  it  contracts. 
The  apparatus  shown  in  Fig.  5  illus- 
trates the  expansion  of  solids.  This 
consists  of  a  brass  ball,  so  made  that, 
at  ordinary  temperatures,  it  will  pass 
easily  through  the  ring,  m.  On  heat- 
ing the  ball,  it  will  no  longer  pass 
through  the  ring. 

This  increase  of  volume  of  a  heated 
body  must  be  due  to  a  motion  among 
the  molecules,  which  tends  continually 
to  separate  them.  When  this  motion 
increases  in  intensity,  the  body  be- 
comes warmer;  when  this  motion  decreases  in  intensity,  the 


FIG.  5. 


22  ELEMENTS  OF  PHYSICS. 

body  becomes  cooler.  Hence,  we  may  measure  the  intensity 
of  the  heat,  or  tfie  temperature  of  a  body,  by  the  degree  of 
the  molecular  motion,  or  by  the  expansion  of  bodies. 

33.  The  Thermometer  is  an  instrument  which  measures 
temperatures.  The  ordinary  mercurial  thermometer  consists 
of  a  very  small  glass  tube  (Fig.  6),  at  one  end  of  which 
is  blown  a  bulb  —  the  bulb  and  part  of  the  tube  are 
filled  with  mercury.  When  the  thermometer  is  placed 
near  a  source  of  heat,  the  column  of  mercury  rises,  and 
falls  when  it  is  removed,  because  of  the  expansion  and 
contraction  of  the  mercury.  The  glass  also  expands 
and  contracts,  but  only  one-seventh  as  much  as  the 
mercury;  and  so  we  have  only  to  notice  the  apparent 
expansion  of  the  mercury. 

In  order  to  compare  temperatures,  we  assume  as 
standards  the  temperatures  of  melting  ice  and  of  water 
boiling,  under  the  pressure  of  one  atmosphere.  These 
standards  are  called,  respectively,  the  freezing  and  the 
boiling  points. 

For  greater  convenience,  arbitrary  scales  have  been  devised 
to  designate  small  variations  in  the  mercurial  column.  The 
freezing  and  boiling  points  are  first  determined,  and  the 
height  of  the  column  in  each  case  is  marked  on  the  tube,  or 
on  the  scale  attached  to  it.  The  space  between  these  is  then 
divided  into  any  number  of  equal  parts,  called  degrees,  and 
parts  of  the  same  length  set  off  above  and  below  the  boil- 
ing points. 

The  Centigrade  scale  marks  the  freezing  point  by  0°,  and 
the  boiling  by  100°. 

Reaumer's  scale  marks  the  freezing  point  by  0°,  and  the 
boiling  by  80°. 

FahrenJieit's  scale  marks  the  freezing  point  by  32°,  and 
the  boiling  by  212°. 


MEASUREMENT  OF  HEAT.  23 

These  scales  are  distinguished  by  the  letters  C,  K,  and  F. 
The  divisions  below  zero  are  indicated  by  the  negative  sign. 
Thus,  —10°  signifies  ten  degrees  below  zero;  10°,  or  +10°, 
signifies  ten  degrees  above  zero. 

To  compare  these  scales,  we  first  notice  the  interval  be- 
tween the  freezing  and  boiling  point,  and  find  C  =  100°, 
R=80°,  F=180°;  hence,  these  are  equal,  or  1°  C  = 
4°  R  — 1°  F.  Now,  if  we  remember  that  the  zero  of 
Fahrenheit's  scale  is  32°  below  the  freezing  point,  we  may 
convert  one  scale  into  another,  thus: 

°F  =  J  °R  -f-  32° 

°R=   (°F  —  32°)  f 

°R  =  i°C 

_ 

34.  The  amount  of  heat  in   a  body  must  not  be  con- 
founded with  its  temperature.     It  is  evident  that  a  pint  of 
boiling  water  would  have  the  same  temperature  as  a  gallon 
of  boiling  water,  and  would  equally  affect  a  thermometer. 
The  relative  amount  of  heat  present  in  a  body  is  measured  by 
the  thermal  unit.     This  is  the  quantity  of  heat  required  to 
raise  a  pound  of  water  from  32°  F.  to  33°  F.      Hence,  a 
gallon  of  boiling  water  would  contain  eight  times  as  many 
thermal  units  as  a  pint,  and  would  be  competent  to  melt 
eight  times  as  much  ice  or  snow. 

35.  The  force  of  light  is  closely  related  to  that  of  heat. 
It  may  seem  strange  that  it  is  reckoned  as  a  force ;  but  it  is 
easy  to  show  that  it  may  produce  change  in  matter.     Thus, 
if  the  gases  hydrogen  and  chlorine  are  mixed  in  equal  quan- 
tities in  the  dark,  they  will  not  combine;  but  if  exposed  to 
the  free  sunlight,  they  will  unite  with   explosive  violence. 
The  photographer's  art  depends  on  the  force  of  light.     Soak 
a  strip  of  white  newspaper  in  common  salt  brine  and  let  it 
dry;  when  dry,  again  moisten  it  in  a  darkened  room  with  a 


24 


ELEMENTS  OF  PHYSICS. 


sponge  dipped  in  a  solution  of  silver  nitrate,  and  again  dry 
it.  This  process  covers  the  paper  with  white  silver  chloride. 
Now  if  this  coated  paper  be  placed  in  the  sunlight,  it  will 
darken,  showing  that  the  light  effects  a  change  in  the  silver 
chloride.  Moreover,  in  the  grand  laboratory  of  nature,  light 
is  an  essential  force.  To  define  it,  we  select  one  of  its  prop- 
erties and  say  that  "light  is  that  mode  of  motion  which  ex- 
cites in  us  the  sensation  of  vision." 

36.  The  force  of  electricity  is  familiar  to  all,  in  its  ap- 
plications to  the  telegraph,  in  the  magnet,  and  in  the  flash 
of  lightning. 

Its  simplest  effects  may  be  shown  by  rubbing  a  glass  rod 
briskly  upon  the  coat-sleeve,  and  then  presenting  the  rubbed 
end  to  small  and  dry  pieces  of  paper.  If  the  air  is  not  too 
damp,  the  paper  will  be  attracted  to  the  rod,  cling  to  it  for  a 
little  while,  and  then  fly  off. 
Instead  of  the  bits  of  paper, 
we  may  employ  a  light  pith 
ball,  suspended  by  a  silk 
thread,  Fig.  7.  The  ball  will 
be  first  attracted  and  then 
repelled  by  the  excited  rod. 
We  may  use  this  phenomenon 
to  define  electricity  as  a  force 
which  becomes  manifest  by 
its  peculiar  phenomena  of 
attraction  and  repulsion. 

37.  These  are  the  only  forces  of  inanimate  nature  of 
which  we  have  any  certain  knowledge. 

They  produce,  by  their  action  upon  matter,  secondary 
forces,  which  are  employed  by  man  in  machines.  Thus,  the 
strength  and  elasticity  of  springs  is  mainly  due  to  cohesion ; 
the  action  of  glues  and  cements,  to  adhesion;  the  elastic 


FIG.  7. 


CONSERVATION  OF  FORCE.  25 

force  of  steam,  to  heat;  the  power  of  running  water,  or  of 
falling  weights,  to  gravitation;  the  muscular  strength  of 
men,  to  cohesion,  affinity,  etc.,  modified  by  the  vital  forces. 

38.  However  forces  act  upon  bodies,  the  matter  of 
which  they  are  composed  is  not  lost.  When  gunpowder  is 
exploded,  it  disappears,  leaving  only  for  a  moment  a  trace  of 
smoke.  It  has,  however,  only  undergone  a  chemical  change, 
by  which  a  part  of  its  ingredients  have  been  converted  into 
gases.  If  the  explosion  is  made  in  a  sealed  vessel,  suffi- 
ciently strong  to  stand  the  shock,  the  vessel  and  its  contents 
will  not  change  in  weight  by  the  operation.  Matter  is  in- 
destructible by  any  force  that  man  can  employ  upon  it. 

We  are  also  justified  in  asserting  that  force  is  indestruct- 
ible. Affinity,  electricity,  heat,  arid  light,  are  so  closely 
allied  that  the  action  of  any  one  may  induce  the  action  of 
any  other :  thus  a  candle  burns  by  reason  of  affinity,  and 
gives  out  heat  and  light.  For  this  reason  these  four  are 
called  correlative  forces. 

NATURAL  PHILOSOPHY  OR  PHYSICS  treats  of  the  physical 
changes  which  are  produced  by  the  action  of  force  upon 
matter. 

RECAPITULATION. 

Bodies  are  classified 

f  Solid,  as  ice. 
I.    With  regard  to  state  as  •<  Liquid,  as  water. 

(.  Aeriform,  as  steam. 

TT     iTT-i.i-  f  Simple,  as  oxygen. 

II.    With  regard  to  composition,    •< 

(  Compound,  as  water. 

Forces  act 

I.  Only  on  molecules,  II.  Also,  on  bodies, 

C  Cohesion, 
-j  Adhesion. 
(.  Affinity. 

Gravitation. 
PHYS.  3. 


Also,  on  OOQL 
/  Electricity. 
I  Light. 
j  Heat. 
'   Gravitation. 


26  ELEMENTS  OF  PHYSICS. 

'  The  general  properties  of  matter  are— magnitude,  weight,  impene- 
trability, mobility,  inertia,  divisibility,  porosity,  compressibility,  ex- 
pansibility. 

We  estimate  the  action  of  forces  by  certain  units.  Among  these 
are  units  of  measure,  units  of  volume,  units  of  time,  units  of  weight, 
units  of  pressure,  units  of  heat. 

PROBLEMS. 

1.  How  many  centimetres  are  there  in  29.922  inches? 

2.  How  many  inches  are  there  in  0.994  metres? 

3.  How  many  square  inches  are  there  in  a  circle  of  one  inch  radius? 
of  two  inches  radius?    What  is  the  ratio  between   the  two  areas? 
How  many  square  centimetres  are  there  in  each  circle  ? 

^4,  How  many  cubic  inches  are  there  in  one  pint?  How  many 
cubic  centimetres?  How  many  litres? 

"N^  How  many  litres  are  there  in  a  sphere  of  six  inches  radius?  of 
one  foot  radius?  What  is  the.  ratio  between  the  two  volumes?  How 
many  gallons  are  there  in  each  sphere  ? 

6.  What  will  be  the  weight  of  each  sphere   if  made   of  air?    of 
water?  of  gold?    Reckon  each  in  pounds  and  also  in  grammes. 

7.  What  will  be   the   edge  of   a   cube  containing   ten   pounds   of 
water?  the  radius  of  a  sphere  containing  an  equal  weight  of  water? 

8.  From  the  table  of  specific  gravities  calculate   the   weight  of  a 
gallon  of  oxygen,  of  sulphuric  acid,  of  cork,  of  silver. 

9.  What  does  a  litre  of  dry  air  weigh  in  grammes? 

10.  What  is  the  average  velocity  per  minute  of  a  locomotive  that 
passes  over  138  miles  in  six  hours? 

11.  What  will    be   the  atmospheric    pressure   on  a  surface    of   six 
square  inches  in  pounds?  in  grammes?    On  a  surface  of  six  inches 
square,  in  pounds?    in  kilogrammes? 

12.  What  is  the  atmospheric  pressure  on  one  square  centimetre  in 
kilogrammes  ? 

13.  Convert  25°  C.  to  °F. ;   50°  C.  to  °F.    Can  you  say  that  50°  C. 
is  twice  as  hot  as  25°  C.  ? 

14.  Convert  62°  F.  to  °C. ;   39°.2  F.  to  °C. 

15.  If  a  gallon  of  boiling  water  will  melt  ten   pounds  of   ice,  how 
mucfc  will  be  squired  to  melt  one  cubic  foot  ? 


CHAPTER  II. 

PHENOMENA    CONNECTED    WITH    COHESION. 

39.  The  cohesion  of  solids  may  be  estimated  by  the 
resistance  which  they  offer  to  forces  which  tend  to  separate 
their  particles. 

There  are  many  ways  by  which  the  strength  of  a  body 
may  be  tried.  Among  these  are : 

(1)  By  a  stretching  force. — We  may  hang  a  rubber  tube 
from  a  hook,  and  pull  it  downward  by  a  weight.    The  rubber 
will  stretch,  and,  with  a  weight  sufficiently  heavy,  will  be 
torn  in  pieces.    The  strength  which  a  body  offers  to  a  stretch- 
ing force  is  called  its  tenacity.     The  tenacity  of  metals  is  in- 
creased by  drawing  them  into  wires.    A  cable  made  of  wires 
twisted  together  is  far  stronger  than  a  chain  of  equal  weight. 
Wire  cables  are  used  in  suspension  bridges  for  this  reason. 
The  suspension  bridge  at  Cincinnati  has  a  span  of  one  thou- 
sand feet. 

(2)  By  a  compressing  force. — If  we  place  a  weight  on   a 
small  bar  of  wood,  it  will  compress  its  particles  and  tend  to 
crush  the  bar.     When  the  bar  is  not  allowed   to   bend,   it 
offers  the  same  resistance  to  pressure   that  it  would  to  a 
stretching  force. 

(3)  By  a  bending  force. —  If  we  fasten  one  end  of  a  lath, 
placed  horizontally  in  a  vice,  and  apply  a  weight  at  the  other 
end,  it  will  bend  and  tend  to  break.    The  strength  which  the 
substance  exhibits  depends  not  only  on  the  material  but  also 
on  the  manner  in  which  the  strain  is  applied.     A  sudden 
shock  causes  a  much  greater  strain  than  a  gradually  increas- 
ing force  of  greater  amount.     So,  also,  the  lath  will  support 

(27) 


28  ELEMENTS  OF  PHYSICS. 

a  greater  weight  when  its  broad  side  is  placed  vertically  than 
when  it  is  horizontal;  then,  also,  the  longer  it  is  the  less 
weight  it  will  support.  Finally,  if  both  ends  are  supported, 
it  will  sustain  half  the  weight,  when  it  is  concentrated  at  the 
center,  that  it  will  when  distributed  along  its  whole  length. 
What  is  true  of  the  lath,  is  also  true  of  the  beams  used  in 
houses,  they  are  placed  so  as  to  receive  the  strain  on  their 
edges. 

The  bones  of  animals,  and  the  stalks  of  grain,  are  hollow. 
This  is  the  most  economical  arrangement  of  a  given  weight 
of  material.  We  may  illustrate 
this  fact  by  resting  the  ends  of 
a  flat  sheet  of  paper  on  bricks, 
and  ascertaining  the  force  neces- 
sary to  break  it  down ;  then  re- 
peat the  test  with  a  similar  sheet 
of  paper  after  having  coiled  it 
into  a  tube,  Fig.  8.  If  a  broad  FlG>  8- 

strap  is  used  to  hang  the  weight  from,  a  closely  coiled  tube 
of  this  sort  will  support  three  or  four  times  as  much  weight 
as  before.* 

(4)  By  a  twisting  strain. — Suppose,  when  the  lath  is  in  the 
vice,  we  attempt  to  twist  it.  The  force  will  tend  to  wrench 
the  particles  asunder;  and  it  is  possible  that  we  may  ac- 
complish this  with  a  long  and  thin  lath.  The  kind  of 
strength  that  resists  a  twisting  strain  is  called  resistance 
to  torsion. 

40.  The  effective  strength  of  any  structure  is  that  which 
is  not  employed  in  supporting  the  weight  of  the  structure  itself. 
It  would  be  impossible  to  build  such  roofs  and  bridges  of 
iron  as  have  been  built  of  wood,  because  the  strength  of  the 
material  would  not  be  sufficient  to  support  its  own  weight. 
Pine,  which  has  nearly  half  the  tenacity,  has  only  one-tenth 


ANNEALING.  29 

the  weight  of  iron ;  so  that,  for  equal  weights,  pine  has 
more  than_  four  times  the  tenacity  of  cast-iron.  Steel  has 
the  greatest  tenacity  known.  A  rod  of  steel,  one  foot  long 
and  a  square  inch  in  area,  will  support  a  weight  of  130,000 
pounds. 

41.  If  a  body  does  not  give  way  on  the  application  of 
a  strain,  it  is  frequently  permanently  changed  in  shape.     A 
stretching  force  may  draw  some  bodies  into  a  wire-shape. 
Such  bodies  are  ductile.  (Glass  is  very  ductile  when  at  a  red 
heat,  and  may  be  drawn  into  very  delicate  threads.    A  com* 
pressing  force  flattens  some  bodies  into  thin  sheets.      Such 
bodies  are  malkable.     Most  metals  are  both  malleable  and 
ductile,   though   not   in   equal   degrees.     Gold   is  the  most 
malleable,  and  platinum  the  most  ductile  of  metals. 

42.  A  sudden  blow  often  breaks  many  bodies  that  in 
other  respects  are   quite   strong.      Such   bodies  are  brittle. 
Glass  is  a  good  example.     A  bottle  that  will  resist  a  great 
pressure  is  broken  by  a  gentle  blow  from  some  hard  sub- 
stance.    A  hard  substance  is  frequently  also   brittle.     We 
measure   the    hardness    of   a    body    by    the   readiness   with 
which  it  is  scratched  by  another  substance.     The  diamond 
is   the   hardest   body-v  known.      Quartz  is   hard   enough   to 
scratch  glass.          y/J?/?  /     JrfY  ££?£ 

43.  When  steel  is  strongly  heated,  and  then  suddenly 
cooled,  it  becomes  very  hard,  and  so  brittle  that  it  is  suit- 
able only  for  the  dies  used  in  coining,  and  for  the  hardest 
files.     On  the  other  hand,  if  it  is  cooled  slowly,  it  becomes 
softer,  more  ductile,  and   tenacious.     This  process  of  slow 
cooling  is  called  annealing.     Steel  is  tempered  by  first  harden- 
ing it,  and   then   a  portion  of   its  hardness  is  removed  by 
reheating  the  steel  to  a  lower  temperature  than  at  first,  and 
then  cooling  it  gradually.     The  temper  required  depends  on 
the  use  to  which  the  steel  is  to  be  applied.     Surgical  instru- 


30  ELEMENTS  OF  PHYSICS. 

ments  require  a  hard,  keen  edge ;  table  knives  require  more 
flexibility ;  and  springs  require  both  flexibility  and  tenacity. 
The  effect  x>f  rapid  or  slow  cooling  in  glass  is  about  the 
same  as  in  steel.  Melted  glass  dropped  into  water  solidifies 
into  the  curious  toy  known  as  Prince  Rupert's  drops,  Fig.  9. 
The  body  of  these  drops  is  so  hard  that  it  will  bear 
a  smart  blow ;  but  if  the  tail  be  broken,  the  whole 
flies  into  minute  particles.  This  brittleness  is  pre- 
vented in  glass  utensils  by  carefully  annealing.  As 
soon  as  the  glass  vessels  are  blown,  they  are  drawn 
through  a  long  furnace  in  which  the  heat  gradually  FlG>  9* 
diminishes  from  one  end  to  the  other.  The  thicker  the 
glass,  the  longer  the  time  required  in  annealing." 

44.  The  phenomena  just  considered  involve  a  perma- 
nent displacement  of  the  particles  of  a  body.     If  the  strain 
does  not  exceed  a  certain  limit,  the  body  will  resume  its 
previous  shape,  when  the  force  has  ceased  to  act.    The  en- 
ergy with  which  the  particles  resume  their  original  position 
is  due  to  their  elasticity.     Up  to  the  limit  of  elasticity,  the 
elastic  force  is  exactly  equal  to  the  strain,  and  the  elasticity 
is  therefore  perfect.    Beyond  this  limit,  brittle  bodies  break : 
the  molecules  of  most  other  solids  are  permanently  displaced, 
or  set-,  with  new  relations  to  elasticity,  exactly  similar  to  the 
first.     Thus :    when  a  wire  has  been  permanently  lengthened 
by  a  great  strain,  it  is  still  enabled  to  manifest  perfect  elas- 
ticity by  recovering  from  a  smaller  strain. 

Flexibility  should  not  be  confounded  with  elasticity.  A 
\vire  of  soft  iron  is  very  flexible,  though  but  slightly  elastic ; 
that  is,  it  may  be  readily  bent,  but  does  not  recover  its  posi- 
tion when  the  force  is  removed.  A  steel  spring  is  both  flex- 
ible and  elastic. 

45.  The  elasticity  developed  by  compression  belongs  to 
all  bodies,  whether  solids,  liquids,  or  gases.    All  fluids  are  per- 


ELASTICITY.  31 

fectfy  elastic.  Liquids  are  but  slightly  reduced  in  volume  under 
ordinary  pressures.  Gases  decrease  in  volume  as  the  pressure 
exerted  upon  them  increases;  if  the  pressure  be. doubled,  the 
volume  will  be  one-half,  etc.  When  the  pressure  is  removed, 
both  liquids  and  gases  resume  their  original  volume. 

The  elasticity  of  aeriform  bodies  is  exemplified  by  a  boy's 
pop-gun.  The  air  between  the  wad  and  the  piston  increases 
in  elastic  force  as  it  decreases  in  volume,  until  the  elasticity 
is  sufficient  to  expel  the  wad. 

The  elasticity  of  such  solids  as  India  rubber,  ivory,  and 
steel,  is  very  great.  If  a  ball  of  ivory  or  of  glass  be  dropped 
on  a  slab  of  marble,  it  will  rebound  to  a  height  nearly  equal 
to  that  from  which  it  fell.  If  the  slab  had  been  covered 
with  oil,  it  would  be  found  that  the  ball  had  left  a  circular 
impression  on  the  plate,  and  had  itself  received  a  blot  of 
oil.  On  repeating  this  experiment,  it  will  be  seen  that  the 
size  of  the  spot  on  the  slab  and  on  the  ball  increases  with 
the  height  from  which  it  falls.  It  appears,  therefore,  (1) 
that  the  ball  was  compressed  at  the  moment  of  the  shock ; 
(2)  that  the  rebound  was  caused  by  the  effort  to  regain  its 
shape ;  (3)  that  the  elastic  force  increases  with  the  strain. 

Lead,  clay,  and  the  fats  receive  a  set  with  only  a  moderate 
compressing  force,  and,  therefore,  have  but  little  elasticity. 

46.  The  elasticity  of  musical  strings   is  developed   by 
stretching.      The  tendency  that  twisted  strings  have  to  un- 
twist exemplifies  the  elasticity  developed  by  torsion.     The 
elasticity,  developed  by  bending,  is  splendidly  shown  in  glass 
threads :    in  them  it  is  perfect,  as  they  never  receive  a  set, 
but  break  when  the  limit  of  elasticity  is  passed. 

47.  The  practical  applications  of  elasticity  are   innu- 
merable.    The  elasticity  of  solids  is  applied  in  the  springs 
used  in  watches,  clocks,  carriages,  bows,  spring-balances,  etc. 


32  ELEMENTS  OF  PHYSICS. 

The  elasticity  of  air  is  turned  to  account  in  foot-balls,  air- 
cushions,  air-springs,  etc. 

RECAPITULATION. 

The  properties  which  have  been   considered  in  this  chapter  are 
called  the  specific  properties  of  bodies.    They  fall  into  two  classes : 

Tenacity, 


I.  Those  involving  strain  of  particles, 


Resistance  to  pressure, 
Resistance  to  bending, 


Resistance  to  torsion, 
Elasticity. 

(Ductility, 
Malleability, 
Hardness, 
Brittleness. 


CHAPTEK  III. 


PHENOMENA    CONNECTED    WITH   ADHESION. 

48.  The  force  of  adhesion  gives  value  to  cements :  thus 
glue  is  used  for  wood ;  gum  mastic  and  shellac  for  glass ;  dex- 
trine for  paper;  etc.     This  choice  of  cements  for  different 
objects  shows  that  adhesion  varies  with  the  kind  of  matter. 

Some  of  the  phenomena  of  adhesion  have  received  specific 
names,  and  are  of  great  importance.  Among  these  are  the 
following : 

49.  Capillary  action. —  If  a  clean  glass  plate  is  dipped 
vertically  in  water,  the  liquid  will  rise  on  each  side  to  the 
height  of  nearly  one-sixth  of  an  inch, 

Fig.  10.  It  must  be  evident  that  the 
weight  of  this  liquid  column  is  sup- 
ported by  the  adhesion  of  the  water 
to  the  glass.  A  second  plate  will  sup- 
port an  equal  weight;  and,  hence,  if 
two  parallel  plates  are  brought  so  near  ^ 
each  other  that  both  may  act  on  the  i 


same    molecules    of    the    liquid,    the  Fia  10> 

column  of  the  water  will  rise  higher. 
The  nearer  the  plates,  the  higher  will 
the  liquid  rise,  Fig.  11.  Two  plates,  one- 
hundredth  of  an  inch  apart,  will  sup- 
port a  column  of  water  two  inches  high. 
When  two   plates   are   inclined   to- 
ward each  other,  as  in  Fig.  12,  the  FIG.  11. 
water  takes  the  shape  of  the  curve  known  as  the  equilateral 
hyperbola. 

(33) 


34  ELEMENTS  OF  PHYSICS. 

Finally,  if  a  tube  is  substituted 
for  the  plates,  the  molecules  of 
the  liquid  will  be  attracted  on  all 
sides,  and  the  water  will  rise  to 
twice  the  height  produced  by 
two  plates,  separated  by  a  space 
equal  to  the  diameter  of  the  tube. 
If  the  tube  has  a  diameter  of  one- 
hundredth  of  an  inch,  the  column 
of  water  will  be  four  inches  high.  FIG.  12. 

50.  The  adhesion  which  causes  liquids  to  rise  on  solids 
is  called  capillary  attraction,  because  it  is  best  exhibited  in 
very  small  hair-like  tubes. 

Liquids  do  not  rise  in  tubes  unless  they  wet  them ;  if  they 
do  not  wet  them,  they  are  depressed.  A  needle,  slightly 
greased,  can  be  made  to  float  on  water,  because,  not  being 
wet  by  the  liquid,  it  produces  a  depression  in  which  it  is 
supported.  For  the  same  reason  mercury  is  depressed  by  a 
glass  plate,  but  rises  freely  on  lead  and  some  other  metals. 
The  amount  of  ascent  and  depression  varies  with  the  sub- 
stances used:  thus,  in  a  glass  tube,  alcohol  will  rise  about 
one-half  as  much  as  water  —  mercury  is  depressed  in  a  glass 
tube,  and  its  surface  is  convex,  while  water  exhibits  a  con- 
cave surface. 

51.  Familiar  illustrations  of  capillary  attraction  are 

seen  in  the  action  of  lamp-wicks.  Blotting  paper  readily 
draws  ink  into  its  pores,  which  resemble  short  capillary 
tubes.  The  pores  in  writing  paper  are  closed  by  sizing.  If 
One  end  of  a  towel  is  dipped  in  a  basin  of  water,  and  the 
other  left  hanging  over  the  edge,  the  Avhole  towel  will  be- 
come wet.  Water  can  not  be  poured  out  of  a  full  tumbler 
without  running  down  the  outside  because  of  the  adhesion 
of  the  water  to  the  glass. 


SOLUTION.  35 

In  the  droughts  of  summer  the  water  necessary  to  the 
support  of  vegetation  is  drawn  toward  the  surface  of  the 
ground  by  capillary  action.  It  is  also  one  of  the  principal 
causes  of  the  ascent  of  sap  in  plants,  and  plays  an  essential 
part  in  the  circulation  of  liquids  in  animal  tissues. 

52.  Solution.  —  If  a  lump  of  sugar  is  dipped  in  water, 
the  liquid  will  rise  by  capillary  attraction  until  the  whole 
is  moistened.     If  enough  water  is  present,  the  sugar  will 
entirely  disappear   in   the   liquid,   thus  forming  a   solution. 
This  shows  that  the  adhesive  force  is  sometimes  sufficient  to 
overcome  the  cohesion  of  solids.     Each  drop  of  the  solution 
is  sweet  like  sugar,  and  fluid  like  water,  showing  that   the 
adhesion  is  perfect,  because  it  is  shared  by  every  molecule. 
A  solution  is  said  to  be  saturated  when  no  more  of  the  solid 
will  dissolve  in  it. 

53.  The   solvent    powers  of  liquids  vary  exceedingly. 
An  ounce  of  cold  water  will  dissolve  two  ounces  of  sugar, 
although  it  can  dissolve  hardly  a  grain  of  sulphate  of  lime. 
Fats  dissolve  in  ether,  benzine,  and  bisulphide  of  carbon; 
resins  dissolve  in  alcohol ;  lead  and  gold  in  mercury. 

When  a  metal  disappears  in  an  acid,  as  copper  in  nitric 
acid,  the  action  has  two  stages:  (1)  a  chemical  action  by 
which  the  solid  and  liquid  unite  to  form  a  substance  differ- 
ent from  either,  as  nitrate  of  copper;  (2)  a  simple  solution 
by  which  the  compound  thus  formed  dissolves  in  the  liquid. 

54.  Gases  also  dissolve  in  liquids. —  The  rapidity  with 
which  water  absorbs  ammonia  may  be  prettily  shown  by  the 
following  experiment :  having  fitted  a  glass  tube,  tapering  at 
one  end,  to  the  cork  of  a  large  bottle,  fill  the  bottle  with 
dry  ammonia  gas.     Then  invert  the  bottle  in  water,  Fig.  13. 
After  a  little  time  the  water  will  absorb  so  much  of  the  gas 
as  to  leave  a  partial  vacuum  in  the  bottle;   the  pressure  of 


36 


ELEMENTS  OF  PHYSICS. 


FIG.  13. 


the  atmosphere  will  then  force  the  water  up 
the  tube  and  form  a  small  fountain. 

One  volume  of  water  absorbs  1049  volumes 
of  ammonia,  506  volumes  of  hydrochloric  acid, 
and  nearly  twice  its  volume  of  carbonic  acid. 

55.  The  weight  of  any  gas  absorbed  by 
a  liquid  varies  with  the  pressure;  that  is,  if 
the  pressure  be  doubled  or  tripled,  the  weight 
of  the  gas  absorbed  will  be  doubled  or  tripled. 
The  effect  of  pressure  on  a  gas  is  to  diminish 
its  volume  and  increase  its  weight  in  propor- 
tion   to    the    pressure.     Therefore   the  volume    of   the  gas 
absorbed  is  the  same  for  all  pressures.      If  the  pressure  is 
removed,  the  gas  resumes  its  original  density,  and  escapes 
with  effervescence.      The  "soda  water"  of  the  confectioner 
is  water  charged  with   carbonic  acid   gas,  absorbed   under 
pressure.  \x 

56.  Porous  solids  like  charcoal,  dry  clay,  and  metals  in 
a  state  of  fine  division,  often  absorb  large  amounts  of  gases. 
One  volume  of  charcoal  will  absorb  35  volumes  of  carbonic 
acid,  and  90  of  ammonia.     A  piece  of  freshly  burned  char- 
coal, exposed  to  the  air  for  a  few  days,  will  often  increase 
one-fifth  in  weight.    This  phenomenon  can  be  explained  by 
the  supposition  that  the  solid,  by  reason  of  its  porous  condi- 
tion, offers  a  very  large  extent  of  surface,  to  which  the  gases 
adhere,  and  become   condensed.      Finely  divided  platinum 
absorbs  250  times  its  volume  of  oxygen. 

57.  The  absorptive  power  of  charcoal  is  of  great  eco- 
nomic value.    The  variety  known  as  bone-black  is  used  for 
clarifying  sugar.     The  brown  sirups  are  filtered  through  a 
layer  of  bone-black  twelve  or  fourteen  feet  in  thickness,  and 
are  thus  obtained  perfectly  clear,   all  the  coloring  matters, 
whether  solid  or  liquid,  being  perfectly  absorbed.     Ale  and 


DIFFUSION.  37 

porter  filtered  through  animal  charcoal  lose  much  of  their 
bitterness,  and  all  of  their  gases.  All  varieties  of  charcoal 
are  efficacious  in  absorbing  the  gaseous  products  of  decaying 
animal  matters,  and,  thereby  removing  noxious  effluvia  from 
the  air. 

58.  Solids  also  adhere  to  gases.  —  The  transportation 
of  dust  by  the  winds   is  a  proof  of  this.     This  action,   if 
continued  for  a  long  series  of  years,  may  effect  great  physical 
changes,  as  is  seen  in  the  shifting  sands  of  the  deserts,  and 
in   the   sandy  hills,   called  dunes,   that   are  formed  on  the 
coasts  of  France. 

59.  When  fluids  mix  with  each  other  without  entering 
into  chemical  union,  it  is  because  of  the  mutual  adhesion  of 
their. molecules.     Some  liquids,  like  water  and  alcohol,  or 
glycerine,  are  miscible  in  all  proportions.     If  equal  volumes 
of  water  and  ether  are  shaken  together,  and   then  allowed 
to  stand,  they  will,  in  great  measure,  separate,  each  liquid 
dissolving  about  one-tenth  of  the  other.    The  adhesion  of  oil 
and  water  is  so  feeble  that  they  can  not  be  made  to  mix  per- 
manently by  any  amount  of  shaking  and  stirring. 

Any  two  gases  will  form  a  permanent  mixture 
when  they  are  placed  in  the  same  vessel,  if  they 
do  not  enter  into  chemical  combination. 

60.  The   tendency  of  fluids   to    mix   with 
each  other   is   called   diffusion.      Diffusion   may 
take    place    without    stirring    or    shaking,   and 
even   in   apparent  opposition  to   the   attraction 
of  gravitation.     Thus,  if  a  tall  jar  is  partially 
filled  with  a  solution  of  blue  litmus,  or  water  in 

which  a  red  cabbage  has  been  boiled,  and  sul-       FIG.  n. 
phuric  acid  is  carefully  poured  through  a  long  funnel  (Fig. 
14),  reaching  to  the  bottom  of  the  jar,  the  line  of  separation 
between  the  two  liquids  will  be,  at  first,  distinctly  marked. 


38 


ELEMENTS  OF  PHYSICS. 


Soon  the  acid  will  rise  and  the  water  will  sink,  until  the  two 
are  perfectly  mixed.  This  will,  however,  require  some  time, 
and  the  progress  of  diffusion  may  be  traced  from  hour  to 
hour  by  watching  the  gradual  change  from  blue  to  red. 
This  may  be  repeated  with  any  two  miscible  fluids,  as  cab- 
bage water  and  a  solution  of  caustic  soda. 

61.  The  diffusion  of  gases  may  be  illustrated  by  the 
apparatus  shown  in  Fig.  15,  which  con- 
sists  of   two    bottles,    connected    by   a 

long  glass  tube. 

Fill  the  upper  with  the  lighter  gas, 
as  hydrogen,  and  the  lower  with  a 
heavier,  as  chlorine.  The  greenish  color 
of  the  chlorine  enables  us  to  trace 
its  gradual  ascent.  In  a  few  hours  the 
two  gases  will  mix  perfectly  and  perma- 
nently. This  experiment  should  be 
performed  only  in  a  darkened  room  so 
as  to  avoid  an  explosion. 

The  diffusion  of  gases  is  of  the  greatest 
importance  in  maintaining  the  purity  of 
the  atmosphere.  The  constituents  of  the 
air  are  of  different  specific  gravities,  -_.,i=  ^_J 

and  would  arrange  themselves  with  the  FIG.  15. 

heaviest  at  the  bottom  if  it  were  not  for  this  beneficent  law 
of  nature.  The  carbonic  acid,  a  product  of  decay  and  com- 
bustion, would  be  found  at  the  surface  of  the  earth,  and 
destroy  all  animal  life.  As  it  is,  the  noxious  gases  are 
rapidly  diluted  when  formed,  and  soon  are  so  perfectly  dis- 
seminated through  the  air,  that  chemical  analysis  fails  to 
find  any  essential  difference  in  the  air  of  mountain,  plain, 
or  valley. 

62.  Osmose  is  a  term  used  to  denote  the  diffusion  of 


OSMOSE. 


39 


fluids  when  they  are  separated  by  a  porous  partition  or 
septum.  The  presence  of  the  septum  greatly  modifies  the 
phenomena  of  diffusion. 

Tie  a  glass  tube  to  the  mouth 
of  a  bladder,  Fig.  16,  fill  the 
bladder  with  strong  brine,  su- 
gar sirup,  or  alcohol,  and  then 
immerse  it  in  pure  water.  After 
a  while  it  will  be  found  that  the 
liquid  has  risen  in  the  tube,  and 
that  the  outer  vessel  contains 
some  of  the  substance  that  was 
in  the  interior.  Hence,  a  cur- 
rent has  been  produced  in  two 
directions.  The  one  passing  in- 
to the  bladder  is  called  endos- 
mose;  the  one  passing  out,  exos- 
mose.  The  rate  of  diffusion 
is  greater  in  osmose  than  in 
simple  diffusion. 

Instead  of  the  bladder,  an  inverted  funnel,  having  its 
mouth  closed  by  a  strip  of  any  animal  membrane,  or  by 
parchment  paper,  may  be  used. 

63.  Dialysis  is  the  application  of  osmose  to  the  separa- 
tion  of   mixed   solutions.      If  a   solution   contains  alcohol, 
hydrochloric  acid,  or  crystallizable  bodies  like  sugar,  they 
will  pass  through    the  septum ;    but  gum-arabic,  gelatine, 
and  other  substances  that  do  not  crystallize,  will  not. 

64.  The  osmose  of  gases  may  be  shown  by  a  striking 
experiment. 

Close  the  mouth  of  a  long  glass  funnel  with  a  septum  of 
plaster  of  Paris.  This  may  be  done  by  making  a  moderately 
thick  paste  of  the  plaster  with  water  on  a  plate,  inverting 


FIG.  16. 


40 


ELEMENTS   OF  PHYSICS. 


the  mouth  of  the  funnel  therein,  and  then  suffering  the 
plaster  to  harden.  After  drying  the  septum,  place  the  tube 
in  colored  water,  and  invert  over  the  closed  mouth  a  jar 
filled  with  hydrogen,  Fig.  17.  The 
endosmose  of  the  hydrogen  will  soon 
become  manifest  by  the  escape  of  bub- 
bles through  the  water.  Remove  the 
jar,  and  the  hydrogen  will  escape  from 
the  funnel  in  a  contrary  direction,  as 
may  be  seen  by  the  rise  of  the  water 
in  the  funnel  tube. 

Although  the  nature  of  osmose  has 
not  been  satisfactorily  determined,  it 
is  manifest  from  the  porous  nature 
of  animal  and  vegetable  membranes, 
that  it  must  play  an  important  part  in 
the  operations  of  life.  In  breathing, 
the  lungs  give  out  carbonic  acid  by 
exosmose,  and  absorb  oxygen  by  en- 
dosmose. It  is  probable  that  the  ascent 
of  sap  in  plants,  and  the  various  pro-  FIG.  17. 

cesses  of  secretion  in  animals  are  either  controlled  or  essen- 
tially modified  by  osmotic  action. 

RECAPITULATION. 


The  force  of  adhesion  is  shown  in 
I.  Cements  and  Friction    - 
IT.  Capillary  action 

III.  Solution  of  solids 

IV.  Solution  of  gases 
V.  Absorption  of  gases 

VI.  Shifting  sands     - 
VII.  Diffusion  of  liquids 
VIII.  Diffusion  of  gases 
IX.  Osmose     - 


-  Solids  to  solids. 
Liquids  to  solids. 

-  Solids  to  liquids. 
Gases  to  liquids. 

-  Gases  to  solids. 
Solids  to  gases. 

-  Liquids  to  liquids. 
Gases  to  gases. 

-  Diffusion  through  septa. 


CHAPTER  IV. 

THE   LAWS   OF  MOTION. 

65.  A  body  at  rest  remains  at  rest;    a  body  in  motion 
will  continue   moving  with   uniform  velocity  in   a  straight 
line,  unless  it  is  acted  upon  by  some  external  force.     This 
statement  is  known  as  the  law  of  inertia,  or  as  the  first  law 
of  motion. 

It  is  difficult  to  furnish  examples  which  will  perfectly 
illustrate  this  law.  Our  experience  teaches  us  that  a  body 
will  not  move  unless  some  force  acts  upon  it;  but  that  a 
moving  body  will  continue  in  motion,  is  not  so  self-evident. 
Now  let  us  roll  a  ball  along  the  ground,  then  on  a  smooth 
floor,  then  on  the  ice :  the  fewer  the  obstacles  in  the  way,  the 
more  direct  will  be  its  course,  the  longer  will  it  continue  in 
motion,  and  the  more  uniform  will  be  its  velocity.  So,  also, 
if  we  spin  a  heavy  top  in  the  air,  and  then  in  a  vacuum,  it 
will  continue  moving  much  longer  in  the  latter  case  than  in 
the  former.  All  moving  bodies  on  the  earth's  surface  meet 
with  opposing  forces,  such  as  gravity,  friction,  and  the  resist- 
ance of  the  air.  The  examples  given  above  show  that  the 
more  we  can  reduce  these  opposing  forces,  the  nearer  will  the 
motion  correspond  to  the  law.  If  we  could  conceive  of  a 
body  set  in  motion  by  a  single  impulse,  and  then  left  to 
itself,  its  motion  would  be  in  exact  conformity  to  the  law. 

66.  To  comprehend  the  action  of  a  force,  three  things 
must  be  known.     (1)  The  energy  with  which   it  acts  in  a 
unit  of  time:    this   may  be   expressed  by  the  pressure  it 
exerts,  or  by  its  power  of  doing  work,  and  may  be  repre- 
sented' by  a  straight  line.    (2)  The  direction,  or  the  line  along 

PHYS.  4.  (41) 


42  ELEMENTS  OF  PHYSICS. 

which  it  acts;  and  (3)  the  point  of  application,  or  the  point 
upon  which  it  exerts  its  action.  In  stating  the  theoretical 
action  of  forces,  such  external  forces  as  friction,  and  the 
resistance  of  the  air,  are  generally  left  out  of  account. 
This  fact  must  be  borne  in  mind  when  experiments  are 
made  intended  to  illustrate  the  action  of  forces. 

67.  A  force  which  acts  for  an  instant  and  then  ceases 
to  act  is  called  an  impulsive  force.     Projectiles,  like  bullets 
and  arrows,  are  set  in  motion  by  impulsive  forces.     A  con- 
stant force  acts  with  the  same  energy  without  ceasing.     It  is 
convenient  for  us  to  consider  a  constant  force  as  due  to  an  in- 
finite number  of  equal  successive  impulses,  each  one  of  which 
acts  through -a  very  brief  interval  of  time.    Gravity  is  a  con- 
stant force.     A  locomotive  under  head  of  steam  that  is  kept 
constant  is  another.      A  constant  force  tends  to  produce  a 
velocity  that  increases  at  each  successive  instant.     Thus,  a 
locomotive  starts  slowly,  and  rapidly  increases  its  rate  of 
motion ;    but  after  awhile  it  moves  with   uniform  velocity, 
because    the    friction    and    the   resistance    of   the   air   also 
increase  so  that  they  are  exactly  equal  to  the  motive  power 
of  the  engine. 

68.  Simple  motion  is  produced  by  the  action  of  a  single 
force.     Compound  motion  is  produced  by  the  joint  action  of 
two  or  more  forces.     A  ball  falling  in  a  perfect  vacuum  is 
an  example  of  simple  motion.     A  ball  falling  in  the  open 
air  is  an  example  of  compound  motion. 

It  is  well  to  consider  some  other  examples  of  compound 
motion.  Suppose  a  boat,  impelled  by  oars  on  quiet  water  at 
the  rate  of  four  miles  an  hour,  enters  a  river  whose  current 
is  three  miles  an  hour,  then,  (1)  if  the  boat  go  down  the 
river,  its  speed  will  be  seven  miles  an  hour ;  (2)  if  the  boat 
go  up  the  river,  its  speed  will  be  one  mile  an  hour;  (3)  if 
the  boat  is  rowed  directly  across  the  river,  its  speed  will  be 


COMPOUND  MOTION.  43 

five  miles  an  hour.  Let  AB  be  the  direction  of  the  boat, 
and  AC  the  direction  of  the  current ;  that  is,  let  these  two 
lines  represent  the  motion  that  would  be 
produced  if  only  one  force  were  acting  at  a 


time.     If  both  are  acting  at  the  same  time,      ^K          ' 
the  actual  direction  of  the  boat  will  be  the 


D 


line  AD,  which  is  the  diagonal  of  the  paral- 
lelogram ABCD.  This  line  also  represents 
the  intensity  of  the  joint  action  of  the  two  FlG-  18- 

forces ;    and  the  boat  will   move  as  if  impelled   only  by  a 
single  force  in  the  direction  of  the  line  AD. 

A  single  force  that  represents  the  effect  of  two  forces 
taken  together  is  called  their  resultant.  When  the  forces,  as 
in  the  third  case,  are  at  right  angles  to  each  other,  the  find- 
ing of  their  resultant  is  the  problem  of  finding  the  hypotenuse 
when  two  sides  of  a  right-angled  triangle  are  given. 
Thus,  32 +  42  =  52. 

69.  Illustrations  of  compound  motion.  —  When  a 
steamboat  is  in  motion,  all  the  objects  on  it  partake  of 
the  onward  motion  of  the  boat.  Balls  may  be  thrown  and 
caught  with  the  same  certainty  as  on  shore.  But  the  direc- 
tions which  these  balls  take  when  referred  to  the  ground 
beneath  the  boat  will  be  the  resultants  of  the  motion  of  the 
boat,  and  the  motions  which  the  players  give  to  the  balls. 
So,  also,  an  acrobat  as  easily  goes  through  his  feats  of  skill 
on  the  back  of  a  horse  in  rapid  motion  as  he  would  on  the 
ground. 

Conversely,  when  we  have  the  resultant  of  two  or  more 
forces,  we  may  find  its  components.  As  an  illustration,  take 
the  sailing  of  a  sloop  under  a  wind  oblique  to  the  course  of 
the  boat.  Represent  the  direction  of  the  wind  by  the  line 
Vm.  Its  force  may  be  resolved  into  two  components :  the 
one,  iff,  tangent  to  the  sail,  and  producing  no  effect;  the 


44  ELEMENTS  OF  PHYSICS. 

other,  mn,  perpendicular  to  the  sail.  As  the  sail  is  oblique 
to  the  axis  of  the  boat,  this  force  will  tend  to  give  the  boat 
a  lateral  motion,  called  the  leeway.  Therefore,  this  force  is 
again  decomposed  by  the  keel  and  the  rudder,  and  the  re- 
sultant impels  the  boat  on  its  course. 

These  are  examples  of  the  second  law  of  motion,  which 
is :  If  two  or  more  forces  act  together  on  a  bodij,  each  force  pro- 
duces the  same  effect  as  if  it  were  acting  alone. 


FIG.  19. 

70.  The  measure  of  force. — We  can  now  understand 
that  if  a  given  force,  acting  for  one  second  upon  a  mass,  .will 
generate  a  certain  velocity ;  a  double  force,  acting  for  one 
second,  will  generate  twice  the  velocity.  So,  also,  if  it  re- 
quires a  given  force  to  impart  a  certain  velocity  to  a  mass, 
it  will  require  double  the  force  to  produce  the  same  velocity 
in  twice  the  mass ;  for  if  the  double  mass  were  halved,  and 
half  the  force  applied  to  each?  placed  side  by  side,  the  ve- 
locity'would  be  the  same.  Hence,  the  product  of  the  mass 
by  the  velocity  is  one  measure  of  force.  This  product  is 
called  momentum. 


CIRCULAR  MOTION.  45 

Thus,  the  momentum  of  a  body  weighing  five  pounds,  and 
moving  with  a  velocity  of  four  feet  per  second,  is  twenty. 
That  is,  it  would  require  twenty  units  of  force,  acting  in  the 
opposite  direction  for  one  second,  to  produce  pressure  enough 
to  bring  the  body  to  rest.  The  momenta  of<  large  bodies, 
moving  very  slowly,  are  sometimes  enormous.  The  momenta 
of  icebergs  are  irresistible  by  any  human  power,  even  though 
their  motion  be  so  slow  as  to  be  almost  imperceptible. 

There  is  also  another  measure  of  force*  which  is  termed 
energy,  or  the  power  of  doing  work,  which  we  shall  consider 
hereafter. 

71.  The  unit  of  work  is  the  force  required  to  raise  one 
pound  one  foot  high.     This  is  called  the  foot-pound.     Tfie 
unit  of  power  is  the  force  required  to  raise  one  foot-pound  in 
one  second  of  time.     A  horse-power  is  the  mechanical  value 
of  a  force  capable  of  raising  five  hundred  and  fifty  pounds 
one  foot  high  in  one  second.     Its  work  is,  therefore,  five 
hundred  and  fifty  foot-pounds  in  one  second. 

72.  Circular  motion.  —  It  follows  from  the  first  law  of 
motion  that  a  single  force  will    produce 

motion  in  a  straight  line.    It  follows  from 
the   second   law  that  if  a  moving  body 
deviates    from    its    original    direction,    a 
.second  force  must  be  acting  upon  it.    If  a 
body  moves  in  a  circle,  which   is  a  con- 
stant series  of  deviations  from  a  straight  FIG.  20!" 
line,  it  must  be  acted  upon  by  a  constant  force,  in  addition 
to  the  impulse  which  urges  it  in  a  straight  line. 

If  a  ball  be  whirled  in  a  circle  by  means  of  a  rubber  cord 
held  by  the  hand,  we  feel  the  cord  stretched  by  a  sensible 
force  pulling  outward  —  the  hand  resists  this  by  pulling  in- 
ward. If  the  cord  is  cut,  the  outward  force  will  carry  the 
ball  in  the  direction  of  the  tangent  to  the  circle,  as  AT; 


46 


ELEMENTS  OF  PHYSICS. 


but  when  the  two  forces  are  equal,  the  curve  is  that  of  a 
circle.  Circular  motion  is  produced  by  the  action  of  two 
forces,  one  of  which,  at  least,  is  a  constant  force.  The  force 
that  tends  to  draw  bodies  to  the  center,  is  called  the  centri- 
petal force;  that  which  tends  to  drive  bodies  from  the  center, 
is  called  the  centrifugal  force. 

73.  The  tendency  of  revolving  bodies  to  fly  off  at  a 
tangent  is  easily  illustrated.    A  stone  let  go  from 

a  sling,  the  mud  flying  off  from  the  wheels  of 
a  carriage  in  rapid  motion,  are  examples.  If 
a  glass  globe,  containing  a  little  colored  water 
and  some  mercury,  is  swiftly  revolved  by  a 
twisted  string,  both  fluids  will  be  whirled  away 
from  the  axis;  the  mercury,  having  the  greater 
relative  weight,  will  occupy  the  equator,  with  a 
belt  of  water  on  each  side,  Fig.  21.  In  laundries 
clothes  are  dried  by  placing  them  in  a  wire  basket 
which  is  then  revolved  many  hundred  times  in  a 
minute.  The  centrifugal  force  may  be  made  to  counteract 
gravity:  thus,  if  a  cup  of  water  be  balanced  on  the  inner 
face  of  a  hoop,  by  beginning 
with  a  series  of  short  swings, 
the  cup  and  its  contents  may 
be  whirled  over  the  head  with- 
out spilling  the  water. 

74.  Newton    proved    that 
the  shape  of  the  earth  is  pre- 
cisely that  which   a    globe   of 
plastic  material  would  take  by 
virtue  of  centrifugal  force.  The 
cause  of  the  flattening  of  the 

earth  at  the  poles  may  be  illustrated  by  passing  an  axis 
through  two  thin  hoops  of  tin,  and  then  twirling  them 


FIG.  21. 


FIG.  22. 


ACTION  AND  REACTION. 


47 


round  with  moderate  velocity ;  they  will  take  the  shape  shown 
in  Fig.  22.  Of  course,  the  upper  part  of  the  hoop  must  be 
free  to  slide  up  and  down  on  the  axis. 

75.  The  third  law  of  motion  asserts  that  action  and  re- 
action are  always  equal,  and  are  in  opposite  directions.     When 
a  weight  rests   upon  a  table,  the  table  resists  the  pressure 
with  an  equal  force.     When  a  ball  is  fired  from  a  cannon, 
the  cannon  recoils  with  a  momentum  equal  to  that  of  the 
ball,  but  its  backward  velocity  is  much  less  because  of  its 
greater  weight.     A  bird,   in   flying,  beats  the  air  with  its 
wings,  and  by  giving  a  stroke  whose  reaction  is  greater  than 
the  weight  of  its  body,  rises  with  the  difference.    If  we  could 
imagine  the  bird  beating  its  wings  in  a  vacuum,  there  could 
be    no    reaction,   and    the 

bird  could  not  move.  So, 
in  walking,  we  are  assisted 
by  the  reaction  of  the 
ground  to  the  pressure  we 
exert. 

76.  The    reaction    of 
solids   may  be  shown   by 
balls  hung  from  a  frame 
so    that    their     diameters 
shall     lie     in     the     same 
straight  line. 

Suspend  two  equal  ivory 
balls  from  the  frame,  in 
Fig.  23,  and  let  6  fall  from 
D  upon  b'.  If  both  balls 
were  perfectly  elastic,  b  will 
lose  half  its  velocity  in  com-  FIG.  23. 

pressing  b',  and  the  body  b'  will  destroy  an  equal  amount  in 
regaining  its  shape ;  therefore,  b  will  lose  all  its  velocity  and 


48  ELEMENTS  OF  PHYSICS. 

remain  at  rest.  The  other  ball,  b',  will  acquire  all  the  ve- 
locity of  b,  and  move  to  C,  a  distance,  on  the  other  side, 
equal  to  D. 

If  the  experiment  is  repeated  with  non-elastic  balls  of 
clay,  both  will  move  forward :  the  momentum  of  the  falling 
body  will  be  communicated  to  the  one  at  rest,  and  the  united 
momenta  will  be  equal  to  that  of  the  falling  ball.  They  will 
therefore  rise  to  a  less  distance  than  C. 

77.  When  bodies  strike  a  fixed  plane  they  rebound 
by  reason  of  the  reaction  of  the  plane.  Suppose  a  perfectly 
elastic  ball  falls  from  P,  Fig.  24, 
upon  a  perfectly  elastic  plane, 
AB.  It  will  r*ebound  to  the 
height  from  which  it  fell.  Now 
suppose  it  thrown  in  the  direc- 
tion of  IN,  the  force  of  the  col-  A~ 
lision  at  N  will  be  resolved  into 
two  components :  the  one,  NE,  j^ 

parallel  to  the  plane  AB,  which  FIG.  24. 

represents  its  velocity,  in  the  direction  of  the  plane ;  the 
other  component,  ND,  perpendicular  to  AB,  represents 
the  elastic  force  tending  to  urge  the  ball  in  the  line  NG. 
By  reason  of  these  two  components  the  ball  will  take  the 
direction  NR,  which  is  the  diagonal  of  the  parallelogram 
NERG. 

The  angle  INP  is  called  the  angle  of  incidence;  the  angle 
PNR  is  called  the  angle  of  reflection.  In  the  reflection  of 
perfectly  elastic  bodies,  the  angle  of  incidence  is  always  equal 
to  the  angle  of  reflection.  When  either  body  is  not  perfectly 
elastic,  the  component  NG  will  be  proportionally  smaller; 
hence,  the  body  will  proceed,  after  reflection,  in  a  line  nearer 
the  plane  than  NR,  and  the  angle  of  reflection  will  be  greater 
than  the  angle  of  incidence.  These  facts  may  be  illustrated 


REACTION  IN  SOFT  BODIES.  49 

by  bounding  balls  of  rubber,  ivory,  clay,  putty,  etc. ,  upon  a 
hard  floor. 

78.  The  reaction  in  soft  bodies  is  not  instantaneous, 
and  the  destructive  effect  is  less.  Thus,  if  a  man  leaps  from 
a  height  into  deep  water,  the  reaction  is  the  same  as  though 
he  alighted  on  a  solid  plane,  but  it  is  diffused  through  a 
sufficient  interval  of  time  to  render  it  comparatively  harm- 
less. Even  soft  bodies  require  some  time  for  the  displace- 
ment of  their  particles.  If  the  surface  of  water  be  struck 
sharply  with  the  open  palm,  the  blow  is  met  by  considerable 
resistance.  The  sport  of  "skipping  stones"  on  water  ex- 
emplifies this  power  of  resistance  for  the  moment. 

KECAPITULATION. 

There  are  three  laws  of  motion.  The  first  declares  that  the  appli- 
cation of  force  is  necessary  to  move  a  body  from  a  state  of  rest;  the 
second,  that  if  two  forces  act  upon  a  body  at  the  same  time,  each 
acts  as  if  it  were  acting  alone ;  the  third,  that  the  application  of  "a 
force  requires  the  agency  of  some  external  body. 

PROBLEMS. 

1.  Find  the  resultant  of  two  forces  that  may  be  represented  by  7 
and  11: 

(a)  When  they  act  in  the  same  direction. 
(&)  When  they  act  in  opposite  directions, 
(c)  When  they  act  at  right  angles  to  each  other. 

2.  Find  the  momentum  of   a  body  whose  weight  is  5  tons,  and 
whose  velocity  is  5  "feet  per  minute.    With  what  velocity  must  a 
second  body,  whose  weight  is  5  pounds,  move  in  order  that  it  may 
have  a  momentum  equal  to  that  of  the  first  body? 

3.  How  many  units  of  work  are  required  to  raise  10  cubic  feet  of 
water  34  feet  high? 

4.  How  many  horse -powers  are  required  to   raise  6  cubic  feet  of 
water  each  minute  to  the  height  of  100  feet? 


PHYS.  5. 


CHAPTER  V. 


PHENOMENA    CONNECTED   WITH    GRAVITATION. 

79.  Weight  has  been  defined  as  a  measure  of  the  earth's 
attraction.  If  a  lead  ball  be  suspended  by  a  string,  it  con- 
stitutes what  is  called  a  plumb  line.  If  a 
plummet  hangs  so  that  its  point  touches  the 
surface  of  a  vessel  of  water,  the  line  and 
the  surface  of  the  water  will  be  at  right 
angles  to  each  other,  Fig.  25.  The  direc- 
tion of  the  line  at  any  place  is  called  the 
vertical,  and  a  line  at  right  angles  to  it  is 
called  a  horizontal  line.  If  vertical  lines  are 
drawn  at  different  places  on  the  earth,  they 
will  all  be  directed  toward  the  earth's  center.  Xw-  25- 

Hence,  the  direction  of  ter- 
restrial gravity  is  toward  a 
point  at  or  near  the  center 
of  the  earth,  Fig.  26.  At 
places  near  each  other 
these  verticals  may  be 
^"considered  as  parallel. 

80.    The  center  of 
gravity  is  the  point  about 
which  all  the  parts  of  a 
body  balance  each  other. 
Each  particle  of  a  body  is 
drawn  toward  the  earth's 
center  by  gravity,  and,   hence,  the  effect  of  gravity  on   a 
body,  taken  as  a  whole,  will  be  the  same  as  the  resultant  of 
(50) 


EQUILIBRIUM. 


51 


an  infinite  number  of  equal  and  parallel  forces.  If  we  sus- 
pend a  body  so  that  it  will  hang  freely  from  a  point,  a 
plumb  line  attached  to  the  same  point  will  show  the  direc- 
tion of  this  resultant.  Now,  on  repeating  this  experiment, 
after  suspending  the  body  from  another  point,  a  second 
resultant  will  be  found,  and  the  center  of  gravity  will  be 
the  common  point  of  intersection  of  any  two  resultants. 

81.  When  the  center  of  gravity  is  supported,  the  body 
will  remain  at  rest.     Hence,  (1)  the  weight  of  a  body  may 
be  considered  as  concentrated  in  the  center  of  gravity ;    or 
(2)  the  center  of  gravity  may  be  regarded  as  the  point  of 
application  of  the  force  of  gravity,  since 

it  is  the  only  point  common  to  all  the 
resultants.  The  line  of  direction  of  a 
body  will  be  the  vertical  passing  through 
the  center  of  gravity,  Fig.  27. 

82.  Although  a  body  will  remain 
at  rest,  or  in  equilibrium,  when  its  center 
of  gravity  is  supported,  this  equilibrium 
may  be  one  of  three  kinds : 

(1)  A  body  is  in  stable  equilibrium  if  it 
tends  to  return  to  its   original  position 

after  it  has   been  somewhat   displaced.  Fl&-  27. 

This  will  always  be  the  case  when  any  change  of  position 
elevates  the  center  of  gravity.  A  plumb  line,  when  disturbed, 
finally  comes  to  rest  in  its  original  position. 

(2)  A  body  is  in  neutral  equilibrium  when  it  remains  at  rest 
in  any  adjacent  position  after  it  has  been  displaced.      This 
will  be  the  case  when  the  point  of  support  coincides  with 
the  center  of  gravity,   as  when  a  wheel  is  suspended  on 
its  axle. 

(3)  A   body  is   in  unstable   equilibrium  when    it   tends    to 
depart  further  from   its   original  position  after  it  has  oeen 


52 


ELEMENTS  OF  PHYSICS. 


slightly  displaced.  This  will  be  the  case  when  the  point  of 
support  is  below  the  center  of  gravity.  Thus,  in  Fig.  28,  the 
cone  B  is  in  unstable  equilibrium.  It  may  be  balanced  in 
this  position,  but  the  least  displacement  will  throw  the 


FIG.  28. 

line  of  direction  beyond  the  point  of  support,  and  the  cone, 
will  topple  over.  The  cone  A  is  in  stable  equilibrium,  be- 
cause its  center  of  gravity  is  as  low  as  it  can  be.  The  cone 
C  is  in  neutral  equilibrium,  because  if  it  is  rolled  around 
the  center  of  gravity  will  not  be 
raised  or  lowered. 

The  toy  shown  in  Fig.  29  is  in 
stable  equilibrium,  although  the  fig- 
ure withdut  the  balls  would  be  un- 
stable. The  addition  of  the  balls  has 
the  effect  of  throwing  the  center 
of  gravity  below  the  point  of  sup- 
port. The  same  principle  is  illus- 
trated in  Fig.  30.  A  pail  is  sus- 
pended from  a  stick  lying  on  the 
edge  of  a  table,  and  a  second  stick, 
EG,  is  placed  with  one  end  against 
the  corner  of  the  pail,  and  the  other 
in  a  notch  cut  in  the  horizontal 
stick  CD.  By  this  contrivance  the 
center  of  gravity  of  the  connected  bodies  is  brought  under 
the  edge  of  the  table,  and  the  whole  is  in  stable  equilibrium. 


FIG.  29. 


STABILITY. 


53 


The  pail  may  now  be  filled  with  water  without  changing  the 
equilibrium. 


FIG.  30. 

83.  The  relation  which  gravity  bears  to  equilibrium 
may  be  shown  by  the  apparatus  represented  in  Fig.  31.     It 
consists  of  a  cork,  through  which  have  been  thrust,  at  right 
angles  to  each  other,  two 

half  knitting  needles  arid 
one  whole  one,  and  sup- 
ported by  two  wine-glasses 
placed  under  one  of  the 
shorter  needles.  By  push- 
ing the  vertical  needle  up 
and  down,  the  position  of  FIG.  si. 

the  center  of  gravity  can  be  altered  at  pleasure,  and  the 
apparatus  brought  into  either  stable  or  unstable  equilibrium. 
This  is  a  case  of  a  body  resting  on  two  points.  A  man  on 
stilts  is  another  — when  at  rest,  he  can  be  only  in  a  state  of 
unstable  equilibrium.  A  man  walking  on  a  tight  rope  uses 
a  long  pole,  which  he  thrusts  from  side  to  side  to  assist  him 
in  keeping  the  center  of  gravity  vertically  over  the  rope. 
A  person  walking  on  the  thin  edge  of  a  plank,  throws  out 
his  arms  for  the  same  reason. 

84.  The   stability   of  a  body  depends   on   the  relation 
which  the  center  of  gravity  bears  to  at  least  three  points 
not  in  the  same  straight  line,  and  on  which  it  is  supported. 


54  ELEMENTS  OF  PHYSICS. 

The  base  of  a  body  is  the  polygon  formed  by  connecting  the 
points  of  support;  as,  for  example,  the  legs  of  a  table. 

A  body  resting  upon  a  base  is  stable,  when  the  line  of 
direction  falls  within  the  base.  The  stability  of  bodies  may 
be  estimated  by  the  force  required  to  overturn  them.  This 
will  be  the  force  required  to  raise  the  entire  body  to  the 
height  that  the  center  of  gravity  would  be  elevated  in  order 
to  bring  the  line  of  direction  beyond  the  base. 

The  diagrams  in  Fig.  32  represent  sections  of  different 
solids  drawn  through  the  center  of  gravity,  G.  To  turn 


FIG.  32. 

any  of  these  bodies  over  the  edge  E,  the  center  of  gravity 
must  be  raised  through  the  height  HT.  A  careful  study  of 
these  figures  leads  to  the  following  deductions: 

(1)  The  stability  of  bodies  of  the  same  height  is  increased 
by  widening  the  base.     The  legs  of  chairs  are  inclined  out- 
ward.    A  child's  high  chair  has  a  very  wide  base.     Candle- 
sticks and  inkstands  have  broad  bases. 

(2)  The  stability  of  bodies  is  increased  by  bringing  the 
center  of  gravity  to  the  lowest  possible  position.     In  load- 
ing a  wagon  or  a  ship  the  heaviest  articles  are  placed  at  the 
bottom.     A  load  of  hay  is  easier  overturned  than  a  load 
of  stone. 

(3)  Of  bodies  having  the  same  height  and  base,  but  of 
dissimilar  figure,  the  pyramid  is  the  most  stable. 

Now  compare  the  sections  of  the  inclined  figures  in  Fig. 
33,  and,  we  may  add, 

(4)  The  stability  of  a  body  is  the  greatest  when  the  line 
of  direction  passes  through  the  center  of  the  base. 


MOVEMENTS  OF  MEN.  55 

(5)  When  the  line  of  direction  falls  without  the  base,  the 
body  will  fall,  because  the  center  of  gravity  is  unsupported. 
The  leaning  towers  in  Pisa  and  Bologna  incline  far  from  a 
perpendicular  position.  In  these  the  line  of  direction  still 


FIG.  33. 

falls  within  the  base;  but  the  visitor  who  sees  them  for 
the  first  time  can  not  help  thinking  that  they  are  likely 
to  fall. 

85.  Practical  applications.  —  The  center  of  gravity  in 
man  lies  between  his  hips;  his  base  is  the  area  inclosed  by 
his  feet.  The  different  attitudes  assumed  by  persons  in 
standing  or  moving  about  are  the  results  of  instinctive  efforts 
to  keep  the  line  of  direction  within  the  base.  A  man  stand- 
ing with  his  heels  against  a  vertical  wall  finds  it  difficult  to 
stoop  to  the  floor  without  falling  forward.  In  running,  or  in 
climbing  a  hill,  the  body  is  thrown  forward,  so  that  its  weight 
may  be  carried  with  less  effort.  In  descending  a  hill,  a  man 
leans  backward,  so  that  his  weight  shall  not  cause  him  to 
fall  forward. 

When  a  person  carries  a  load,  he  endeavors  to  preserve 
the  line  of  direction,  common  to  himself  and  the  load,  with- 
in the  base.  If  a  heavy  load  is  in  the  right  hand,  the  body 
is  inclined  to  the  left,  and  the  left  hand  thrown  out.  If  the 
load  is  equally  divided  between  his  hands,  or  placed  on  his 
head,  there  is  no  tendency  to  lean  to  either  side.  If  the 
load  is  on  his  back,  he  leans  forward;  if  carried  in  his  arms, 
he  leans  backward. 


56  ELEMENTS  OF  PHYSICS. 


RECAPITULATION. 

The  center  of   gravity  is  the  point  in  which   the  weight  of    the 
body  may  be  considered  as  concentrated. 

Equilibrium  is  stable,  neutral,  or  unstable,  according  to  the  posi- 
tion of  the  center  of  gravity. 

Stability  depends  on  the  relation  which  the  center  of  gravity  bears 
to  the  base. 


CHAPTER  VI 


THE   LAWS   OF   FALLING   BODIES. 

86.  Gravitation  has  been  shown  to  produce  pressure; 
we  are  now  to  study  how  it  acts  in  producing  the  motion 
of  falling  bodies.  If  we  attempt  to  experiment  by  dropping 
different  balls  from  a  height,  we  shall  meet  with  many 
difficulties. 

(1)  The  resistance  of  the  air.     Light  bodies,  as 
feathers  and  leaves,  almost  float  in  the  air ;  but  if 
any  two  bodies  whatever,  as  a  coin  and  a  feather, 
be  made  to  fall  through  a  perfect  vacuum,  they 
will  reach  the  ground  in  exactly  the  same  time. 
If  two  bodies  have  the  same  weight,  but  are  of 
different  material,  as  a  lead  bullet  and  a  cork,  the 
difference  in  bulk  will  make  so  great  a  difference 
in  the  resistance  of  the  air  as  to  make  the  cork 
fall  perceptibly  slower.     If  the  bodies  were  of  the 
same  material,  but  of  different  size,  the  resistance 
of  the  air  would  be  slightly  in  favor  of  the  larger 
ball,   although  they  would  reach  the  ground   in       J 
very  nearly  the  same  time.  /  ^ 

(2)  If  we  catch  equal  balls,  dropped  from  dif-     FIG.  34. 
ferent  heights,  we  shall  not  only  find  that  the  swiftest  balls 
are  those  which  have  fallen  through  the  greatest  heights, 
but  that  the  velocity  increases  so  rapidly  that  we  can  not 
readily  measure  the  rate  of  increase  in  a  free  fall.     There 
are  several  methods  by  which  we  may  render   the  initial 
velocity  so  slow  that  it  can  be  accurately  measured.     The 
simplest  of  these  methods  is  that  of  Galileo,  who  first  deter- 

(57) 


58  ELEMENTS  OF  PHYSICS. 

mined  the  law  of  falling  bodies  by  rolling  smooth  balls 
down  a  polished  groove  cut  in  a  plane  which  he  inclined  at 
different  angles  of  elevation.  When  a  body  rests  upon  an 
inclined  plane,  its  weight  or  gravity  is  resolvable  into  two 
portions,  one  producing  pressure  on  the  surface,  and  the 
other  tending  to  produce  motion  down  the  plane.  This 
latter  portion  bears  the  same  ratio  to  the  whole  force  of 
gravity  as  the  height  of  the  plane  does  to  its  length ;  and, 
hence,  we  may  diminish  the  velocity  of  the  ball  at  pleasure 
by  lowering  the  height.  Nevertheless,  only  the  absolute 
motion  will  be  changed ;  the  body  will  pass,  in  successive 
moments,  through  spaces  bearing  the  same  ratio  to  each 
other  as  if  it  fell  freely  through  the  air. 

87.   To  repeat  the  experiment  of  Galileo,  stretch  two 
parallel  wires  between  the  walls  of  a  room,  at  any  conven- 


FlG.  35. 

ient  angle,  as  in  Fig.  35.  On  the  lower  wire  hang  a  weight 
to  a  pulley,  so  that  it  will  move  with  little  friction,  and  on 
the  other  fasten  a  convenient  index,  as  a  bell  or  a  slip  of 
paper,  so  that  it  may  be  struck  by  the  top  of  the  pulley  6. 

Suppose  that  the  inclination  of  the  wire  is  such  that,  in 
the  first  second,  the  pulley  passes  over  the  space  ^s;  in  the 
second,  over  the  space  ss';  in  the  third,  over  s's";  and  so  on. 


LAWS  OF  FALLING  BODIES.  59 

If  we  measure  these  spaces,  taking  that  of  the  first  second 
as  unity,  we  shall  find  that  they  increase  in  the  series  of 
odd  numbers  —  1,  3,  5,  7,  etc. — or  at  the  rate  of  two  spaces 
for  each  second.  This  proves  that  increase  of  velocity  is 
uniform ;  and  that  for  bodies  near  the  surface  of  the  earth 
gravity  is  a  constant  force. 

Let  us  now  see  what  we  have  gained  by  our  experiment. 
(1)  The  spaces  described  by  a  falling  body  increase  in  the 
series  of  odd  numbers  —  1,  3,  5,  7.  Any  term  of  this  series 
is  equal  to  twice  the  number  of  seconds,  minus  one. 

FIRST  LAW. — The  space  described  by  any  falling  body,  in  any 
given  second,  is  equal  to  the  product  of  twice  the  number  of  seconds, 
minus  one,  into  the  space  described  the  first  second. 

(2)  The  velocity  is  all  the  time  increasing  at  the  rate  of 
two  spaces  for  each  second ;  therefore  we  have  the 

SECOND  LAW. — The  velocity  acquired  by  a  falling  body  at  the 
G&d  of  any  given  second  is  equal  to  the  product  of  the  number  of 
seconds  into  twice  the  space  described  the  first  second. 

This  product,  it  must  be  borne  in  mind,  is  the  space  a 
body  would  describe  in  the  next  second  were  gravity  to 
cease  to  act,  and  not  the  space  it  actually  describes. 

(3)  The  total  space  passed  through  at  the  end  of  the  first 
seeond  is  1 ;  at  the  end  of  the  second  second,  1  -j-  3  —  4 ;  at 
the  end  of  the  third  second,  1  -f  3  -f  5  =  9.     This  series  in- 
creases in  the  order  of  the  squares  of  the  number  of  seconds  ; 
therefore  we  have  the 

THIRD  LAW. — Tlie  tojal  space  described  by  a  falling  body  at 
the  end  of  any  given  second  is  equal  to  the  product  of  the  square 
of  the  number  of  seconds  into  the  space  described  the  first  second. 

It  is  evident  that  these  laws  are  true,  not  only  for  any  in- 
clination of  the  plane,  but  also  for  a  free  fall.  If  in  the 
experiment  the  height  of  the  plane  had  been  one  foot  and 


60  ELEMENTS  OF  PHYSICS. 

the  length  sixteen  feet,  the  pulley  would  have  traveled  in  the 
first  second,  one  foot ;  in  the  second,  three  feet ;  in  the  third, 
five  feet,  and  so  on.  Therefore,  a  body  falling  freely 
through  the  air  would  pass,  in  corresponding  time,  through 
sixteen  times  these  spaces;  or,  it  would  fall  in  the  first 
second,  sixteen  feet ;  in  the  second,  forty-eight ;  in  the 
third,  eighty,  etc. 

88.  It  has  been  determined  by  careful  experiment  that, 
at  the  latitude  of  New  York,  a  body  will  fall,  in  a  vacuum 
through  16.08  feet  in  one  second,  and  thereby  acquire  a 
final  velocity  of  32.16  feet.     This  last  value  is  called  the  in- 
crement*  of  velocity  due  to  gravity,  and  is  generally  represented 
by   0  =  32.16.      The   space   passed   over   during   the   first 
second  is  %g  =  16.08.* 

89.  The  velocity  increases  every  second  by  the  quan- 
tity 32.16  feet.     The  velocity  at  the  end  of  the  first  second 
is  32.16 ;  at  the  end  of  the  second,  64.32 ;  at  the  end  of  the 
third,  96.48,  and  so  on.     Now,  the  total  space  fallen  through 
at  the  end  of  the  first  second  is  16.08  feet;  at  the  end  of 
the  second,  64.32  feet;  at  the  end  of  the  third,  144.72  feet, 
etc.     If  we  compare  these  two  series  we  shall  find  that  the 
velocity  vanies  as  the  square  root  of  the  height  fallen  through ;  for 


32.16  :  96.48  ::  1/16.08  :  T/144.72. 
This  is  an  important  law.     The  velocity  which  is  acquired 


%  We  may  employ  formulae  to  express  these  laws  by  representing  the 
space  passed  over  during  any  second  by  s;  velocity  by  v;  the  total 
height  of  the  fall  at  the  end  of  any  given  second  by  S,  and  the  num- 
ber of  seconds  by  t. 

First  law 
Second  law 
Third  law 

On  combining  these  formulae  v  =  Y2yS,  t  =  V2S  +  g,  or  f '  S  -+•  16.08,  etc. 


PROJECTILES.  61 

by  a  body  falling  through  any  given  height  may  be  found 
by  multiplying  the  square  root  of  the  height  by  \g,  or  by 
8.02.  Thus,  a  velocity  due  to  a  fall  of  four  seconds,  or  to 
a  fall  of  (42  X  16.08)  =257.28  feet  is  8.02  1/257.28  =  128.64 
feet. 

90.  If  a  body  be  thrown  upward,  the  direction  of  the 
body  is  opposite  to  that  of  gravity,  and,  consequently,  its 
velocity  will  be  diminished  each  second  by  the  quantity 
#  =  32.16.  Hence,  the  time  of  ascent  is  the  same  as  that 
of  a  falling  body  which  attains  a  final  velocity  equal  to  the 
initial  velocity  of  the  ascending  body.  Further,  if  a  body 
be  projected  upward,  the  height  to  which  it  ascends  is  such 
that  when  it  falls  again,  the  body  will  have  acquired  under 
gravity  during  its  descent  a  velocity  equal  to  that  with 
which  it  started  upward. 

^91.  Examples  of  this  law.  Suppose  an  iron  ball  is 
thrown  upward  with  a  velocity  of  32.16  feet  per  second. 
At  the  end  of  one  second  it  will  come  to  rest  and  begin  to 
fall.  It  will  have  moved  in  this  second  with  an  average 
velocity  of  (32.16  -f  0)  ~  2  =  16.08  feet,  and  hence  will  rise 
to  the  height  of  16.08  feet. 

Now,  suppose  the  initial  velocity  be  doubled,  or  64.32 
feet.  It  will  rise  two  seconds  with  the  average  velocity  of 
(64.32  -f  0)  -r-  2  =  32.16,  and  will  describe  during  the  two 
seconds  32.16  X  2  =  64.32  feet. 

If  the  initial  velocity  be  tripled,  its  average  velocity  will 
be  (96.48  -f  0)  ~  2  =  48.24,  and  the  total  ascent  48.24  X  3 
=  144.62  feet. 

Hence,  with  a  double  velocity  of  projection  it  will  rise 
four  times  as  high,  with  a  triple  velocity,  nine  times  as 
high,  and  so  on.  That  is,  the  heights  to  which  a  body  will 
rise  are  as  the  squares  of  the  velocities  of  projection. 

In  these  examples  the  force  has  been  doing  work,  for  it 


62 


ELEMENTS  OF  PHYSICS. 


has  carried  the  body  through  space  in  opposition  to  the 
constant  force  of -gravity.  Hence,  the  energy  of  the  force 
is  proportional  to  the  square  of  the  velocity.  The  energy  is 
also  proportional  to  the  mass  of  the  body,  for  it  is  evident 
that  it  requires  twice  the  energy  to  raise  two  pounds  that  it 
does  to  raise  one  pound.  Therefore,  the  energy  is  propor- 
tional to  the  mass  multiplied  by  the  square  of  the  velocity. 

To  compute  the  work  done  by  a  projectile  force  in  oppo- 
sition to  gravity,  it  is  sufficient  to  multiply  the  weight  of 
the  body  expressed  in  pounds  by  the  number  of  feet  through 
which  it  is  lifted.  The  fyeight  to  which  the  body  will  rise 
is  equal  to  v2  -~  64.32,  or  to  the  square  of  the  velocity  divided 
by  2g.  Hence,  the  work  of  the  force,  expressed  in  foot- 
pounds, equals  mv2  -=-  64.32. 

In  general,  the  energy  of  a  force  is  equal  to  one-half  the 
product  of  the  mass  into  the  square  of  the  velocity,  or  E  = 
Jrav2. 

The  factor  %mv2  is  also  called  vis  viva,  or  living  force.  It 
expresses  the  work  that  a  moving  body  can  perform  before 
it  is  brought  to  rest,  if  no  additional  force  is  added  to  it ;  as 

for  instance,  the  power     ==3.4___ B 

which  different  cannon 
balls  would  have  to  pen- 
etrate obstacles,  like 
planks,  clay,  etc. 

92.  If  a  projectile 
be  fired  in  a  horizontal 
direction,  its  path  will 
be  due  (1)  to  the  force 
of  the  gunpowder,  and 
(2)  to  the  constant  force 
of  gravity.  In  Fig.  36,  FlG-  3G- 

suppose  the  velocity  due  to  the  powder  to  remain  uniform 
during  four  seconds,  and  to  be  represented  by  equal  spaces 


6\ 


UNIVERSAL  GRAVITATION.  63 

on  the  line  AB,  and  represent  the  accelerating  velocity  due 
to  gravity  by  the  unequal  spaces  1,  3,  5,  7.  The  resultant 
of  these  two  forces  will  be  the  curve  Aahcd,  which  is  called 
a  parabola. 

93.  Universal  gravitation.     Thus  far  we  have  considered 
gravity  as  acting  only  upon  bodies  near  the  earth's  surface, 
and  have  found  that  for  such  bodies  gravitation  is  a  constant 
force  proportional  to  mass.     When  we  consider  the  earth's  at- 
traction upon  remote  bodies,  as  the  moon,  or  the  universal 
gravitation  acting  between  the  heavenly  bodies,   we  must 
take  into  account  not  only  (1)  the  mass  of  each  body,  but 
also  (2)  the  distance  between  the  centers  of  gravity  of  the  two 
bodies.     The  law  of  gravitation,  discovered  in  1666  by  Sir 
Isaac  Newton,  is  usually  stated  as  follows: 

Every  particle  of  matter  attracts  every  other  particle, 
with  a  force  (1)  directly  proportional  to  its  mass,  and  (2)  in- 
versely proportional  to  the  square  of  its  distance.  • 

Whenever  the  distance  between  any  two  bodies  is  consid- 
erable, gravity  must  be  considered  as  a  variable  force  which 
diminishes  as  the  square  of  the  distance  increases.  Thus, 
suppose  a  body  taken  one  thousand  miles  above  the  earth's 
surface,  it  is  five  thousand  miles  from  its  center.  The  force 
of  gravity  will,  therefore,  decrease  in  the  ratio  of  (-f$$$)2 
=  |f.  At  this  distance  a  body  will  weigh  J-f  of  its  surface 
weight,  and  during  a  fall  of  one  second  will  acquire  a  velocity 
of  f|  of  32.16  feet  =  20.6  feet  per  second.  At  the  distance 
of  the  moon,  which  is  about  sixty  times  the  earth's  radius, 
the  attraction  of  the  earth  becomes  (g^) 2  =  -g-gW  an^  </  = 
.00892  feet.  Hence,  were  the  moon  to  fall  toward  the  earth, 
it  would  pass  in  the  first  second  over  only  .053  inch. 

94.  The  earth's  equatorial   radius  is  13 J  miles  longer 
than  the  polar  radius,  and  we  should  expect  from  this  that 
the  force  of  gravity  would  increase  in  going  from  the  equator 


64  ELEMENTS  OF  PHYSICS. 

toward  the  poles.  This  oblateness  of  the  earth  causes  a  gain 
of  -g-J-g-  part  of  the  weight  of  a  body.  The  rotation  of  the 
earth  on  its  axis  causes  another  gain  of  ¥|^  part.  The  sum 
of  these  is  y^,  which  is  the  gain  in  weight  that  a  body 
would  experience  on  being  carried  from  the  equator  to  the 
poles.  Consequently,  the  increment  of  gravity  will  vary 
with  the  latitude,  being  at  the  equator  32.0934  feet;  at 
London,  32.1912;  at  Spitzbergen,  32.2528. 

RECAPITULATION. 

Gravity  is  a  constant  force  when  mass  alone  is  taken  into  account, 
but  is  a  variable  force  when  the  distance  between  two  bodies  varies 
in  a  sensible  ratio.  It  acts  as  a  constant  force  on  all  bodies  at  the 
same  place  on  the  earth's  surface  and  is  a  factor  in  the  phenomena 
of  pressure,  of  falling  bodies,  and  of  projectiles. 

Its  intensity  may  be  measured : 

(1)  By  the  weight  of  bodies. 

(2)  By  the  increment  of  velocity  of  falling  bodies. 

(3)  By  the  vibrations  of  a  pendulum. 

A  force  may  be  measured  (1)  by  the  momentum  or  the  inertia  of 
moving  bodies.  (2)  By  the  energy,  or  the  power  of  doing  work. 

PROBLEMS. 

Suppose  a  body  to  fall  freely  in  a  vacuum: 

1.  How  many  feet  will  it  fall  during  the  fifth  second  ?    The  sev- 
enth?   The  ninth? 

2.  What  will  be  its  velocity  at  the  end  of  the  fifth  second?    The 
seventh?    The  ninth? 

3.  How  far  will  it  have  fallen  at  the  end  of  the  fifth  second  ?    The 
seventh?    The  ninth? 

4.  How  many  seconds  will  be  required  for  a  fall  of  402  feet?      Of 
578.28  feet?    What  will  be  the  final  velocity  attained  in  these  cases? 
What  is  the  ratio  between  these  final  velocities? 

5.  Suppose  a  body  to  be  thrown  upward  with  a  velocity  of  1029.12 
feet  per  second,  to  what  height  will  it  rise?    How  many  seconds  will 
elapse  before  it  will  come  to  rest? 


CHAPTER  VII. 


FIG.  37. 


THE  PENDULUM. 

95.  If  a  heavy  weight  or  bob,  as  J5,  Fig.  37,  be  sus- 
pended from  a  point,  A,  by  means  of  a  fine  string,  it  will 
be  at  rest  only  when  in  the  line 
of  the  vertical  A  C.  If  the  bob 
be  raised  to  B,  it  will  tend  to 
move  through  the  curve  B  C,  pre- 
cisely as  a  ball  would  roll  down 
an  inclined  plane  of  the  same 
height,  H C.  The  force  of  gravity 
will  be  partially  resisted  by  the 
string,  and  the  remaining  compo- 
nent of  gravity  will  force  the  ball 
in  the  line  BT. 

As  the  bob  falls,  it  gradually  gains  in  velocity, 
and,  on  falling  the  height  HC,  acquires  sufficient 
momentum  to  carry  it  very  nearly  to  D,  an 
equal  distance  on  the  other  side  of  the  vertical. 
Thence  it  will  return  toward  B,  to  repeat  the 
vibrations  until  the  resistance  of  the  air  shall 
bring  it  to  rest. 

This  may  be  considered  a  simple  pendulum, 
which,  by  theory,  has  its  weight  concentrated 
in  a  single  vibrating  particle.  The  motion  of 
the  pendulum  from  B  to  D  or  from  D  to  B  is 
called  a  vibration.  The  laws  of  the  vibration 
of  the  pendulum  may  be  found,  experiment- 
ally, by  using  simple  pendulums  of  different 
lengths  and  weights,  as  shown  in  Fig.  38. 

(65) 


FIG.  38. 

PHYS.  6. 


66 


ELEMENTS  OF  PHYSICS. 


96.  The  vibrations   of  a   pendulum   are   caused   by 
gravity  alone ;    hence,  the  time  of  vibration  will  not  vary 
with  the  quantity  or  quality  of  the  weight  suspended.     If 
the  ball  c  be  of  copper  and  d  of  wood  they  will  vibrate  in 
the  same  time.     Neither  will  the  time  of  vibration  vary  to 
a  sensible  amount,  whether  the  arc  through  which  the  bob 
passes  be  large  or  small,  because  any  increase  in  the  length 
of  the  arc  is  so  compensated  by  the  increased  velocity  of  the 
fall,  that  the   same  pendulum  will  describe  an  arc  of  five 
degrees  in  about  the  time  required  for  an  arc  of  five  min- 
utes.    Hence : 

97.  The   time   of  vibration  is  dependent  only  on  the 
length  of  the  pendulum.     If  we  make  one  pendulum,  as  a, 
one  foot  long,  and  another,  as  6,  four  feet  long,  the  first  will 
vibrate  in  one-half   the  time  of  the  other ;  and  if  a  third 
pendulum,  c,  be  nine  feet  long,  the  first  will  vibrate  in  one- 
third  of  its  time ;  that  is,  the  limes  of  vibration  of  any  two  pen- 
dulums are  proportional  to  the  square  roots  of  their  lengths ;  and 
conversely,  the  lengths  of  any  two  pendulums  are  proportional  to 
the  squares  of  their  times  of  vibration. 

At  New  York,  a  pendulum  beating 
seconds  is  39.1  inches  long;  a  half  sec- 
onds pendulum  is  39.1  X  (i)2  =  9.78 
inches ;  of  one  vibrating  once  in  three- 
fourths  of  a  second  is  39.1  X  (J)2  =  22  a, 

inches.  // 

ill 

98.  The  compound  pendulum  con-  /// 
sists  of  a  heavy  bob,  suspended  by  an 
inflexible  bar,  from  a  fixed  point,  Fig. 

39.     In   this,  the  mass  of  the  bob  and 
the  weight  of  the  bar  are  both  to  be  re- 
garded.    In  a  rigid  body,  it  is  manifest  FIG.  so. 
that  those   particles   nearest   the   point   of  suspension    will 


COMPOUND  PENDULUM.  67 

tend  to  vibrate  in  the  shortest  time.  Hence,  a  particle  at  a 
•will  accelerate  a  more  distant  particle  at  b,  and  the  more 
distant  particles  will  retard  those  that  are  nearer  the 
point  of  suspension.  There  will,  however,  be  one  particle, 
as  at  o,  which  moves  at  the  average  rate  of  all,  in  which  the 
tendency  of  the  particles  above  it  to  accelerate  its  motion 
is  exactly  compensated  by  the  tendency  of  the  particles  be- 
low it  to  retard  its  motion.  This  particle  will,  therefore, 
move  as  if  it  were  vibrating  alone,  suspended  by  a  thread 
which  had  no  weight,  thus  fulfilling  the  conditions  of  a 
simple  pendulum.  The  position  of  this  particle  is  called  the 
center  of  oscillation. 

99.  The  length  of  a  compound  pendulum  is  the  dis- 
tance between  the  centers  of  suspension  and  oscillation.     In 
a  uniform  bar,  suspended  from  one  end,  the  center  of  oscil- 
lation will  lie  two-thirds  of  the  length  of  the  bar  from  the 
center  of  suspension. 

100.  The  centers  of  oscillation   and  suspension  are 

mutually  interchangeable.  It  is  this  fact  which  enables  us 
to  determine  the  length  of  a  seconds  pendulum  with  accu- 
racy. We  may  obtain  good  results  by  the  follow- 
ing  simple  apparatus,  Fig.  40.  Make  of  hard 
wood  a  slender  bar  sixty  inches  long.  Mark  the 

position  of  the  center  of  gravity,  which  should  be 

~v 
made  to  correspond  very  nearly  with  the  center  of 

the   bar.     About    39.1  -f-  2  =  19.55    inches  above 
and  below  this  point  insert  two  needles. 

The  bar,  made  to  vibrate  from  either  needle,  will 
vibrate    in    about   one  second.      If  the  vibrations 
from  the  two  centers  are  not  performed  in  the  same 
time,  the  bar  may  be  adjusted  by  elevating  or  de-   W 
pressing  the  center  of  gravity.     This  may  be  done     FIG.  40. 
by  placing  a  coil  of  fine  wire  about  the  bar,  where  patient 


68  ELEMENTS  OF  PHYSICS. 

trial  shall  determine  it  is  needed.  When  the  times  of  vibra- 
tion are  the  same  from  either  point  of  suspension,  the  dis- 
tance between  them  is  the  length  of  the  pendulum.  If  the 
precise  time  of  this  vibration  is  known,  as  well  as  the  length 
of  the  pendulum,  the  length  of  a  seconds  pendulum  can  be 
calculated. 

101.  Suppose  that  we  have  found,  in  this  bar,  that  8  is 
the  center  of  suspension  and  0  the  center  of  oscillation, 
what  effect  will  be  produced  on  adding  weights  ? 

(1)  All  the  matter  of  the  pendulum  may  be  considered 
as  concentrated  at  0.     Hence,  if  we  add  a  weight,  W,  at 
this  point  no  change  will  be  made  in  the  rate  of  vibration, 
although  the  bar  will  have  a  new  center  of  gravity,  as  at  G'. 

(2)  If  the  weight  be  applied  below  0,  as  at  TF',  the  cen- 
ters of  gravity  and  oscillation  will  both  be  depressed,  and 
the  length  of  the  pendulum  increased. 

(3)  If  the  weight  be  applied  between  S  and  0,  as  at  W", 
its  effect  will  be  to  raise  the  centers  of  gravity  and  oscilla- 
tion, and  to  shorten  the  pendulum. 

(4)  If  the  weight  be  applied  above  S,  as  at  TF"',  it  tends 
to  retard   the  vibration  of  the  bar,  because  the  particles 
above  S  move  in  directions  opposite  to  those  below.     The 
time  of  vibration  is  thereby  lengthened,  and,  consequently, 
the  center  of  oscillation  lowered,  while  the  center  of  gravity 
is  raised. 

(5)  If  sufficient  addition  be  made  above  S,  the  center  of 
gravity  may  be  made  to  coincide  with  the  center  of  suspen- 
sion.    The  bar  will  then  be  in  a  state  of  neutral  equilibrium, 
and  if  set  in  motion  will  tend  to  rotate  continually. 

(4  and  5)  Now,  as  we  can  raise  the  center  of  gravity  as 
near  the  center  of  suspension  as  we  please  without  making 
them  coincide,  we  may  so  lower  the  center  of  oscillation 
that  it  shall  be  bdow  the  bar.  The  bar  may  be  made  to 


COMPENSATING  PENDULUM.  69 

vibrate  in  two,  three,  or  even  five  seconds,  which  correspond 
to  the  vibrations  of  pendulums  whose  lengths  are  156.4, 
351.9,  and  977.5  inches.  It  is  on  this  principle  that  the 
metronome  is  constructed. 

102.  The  principle  of  the  pendulum  was  discovered  by 
Galileo   in    1581,   but  it  was   first  employed  in  clocks  by 
Huyghens,  in  1656.     The  utility  of  a  pendulum,  as  a  meas- 
ure of  time,  depends  upon  the  perfect  equality  in  the  times  of 
its   vibration.     It  is,  therefore,   essential   that  the   distance 
between  the  centers  of  suspension  and  oscillation  should  be 
invariable.     In  ordinary  clocks,  heat  tends  to  lengthen  and 
cold  to  shorten  the  pendulum,  and  hence  such  clocks  are 
apt  to  go  too  slow  in  summer  and  too  fast  in  winter.     Clocks 
are  regulated  by  raising  the  bob  to  make 

the  clock  go  faster,   and   by  lowering  the 
bob  to  make  it  go  slower. 

103.  Compensating  pendulums  are  those 
which  are  self-regulating.     They  are  made  of 
two  substances  in  such  proportions  that  the 
change  in  length  of  one  upward  is  exactly 
compensated   by   an   equal  change"   of   the 
other  downward.     The  gridiron  pendulum, 
Fig.  41,  consists  of  a  series  of  five  steel  bars, 
expanding  downward,  and  a  series  of  four 
brass  bars  expanding  upward.     In  this  the 
length  of  the  steel  bars  is  *££•  that  of  the 
brass.     The   seconds    mercurial   pendulum, 
Fig.  42,  has   at  the   end  of  a  steel  rod  a 
cylinder   containing   a   column  of  mercury 
6.7  inches  high. 

104.  The  mode  in  which  the  pendulum  FIG.  41. 

is  applied  to  clocks  is  shown  in  Fig.  42.  The  pendulum 
rod  passing  between  the  prongs  of  a  fork,  /,  communicates 


70 


ELEMENTS  OF  PHYSICS. 


FIG.  42. 


its  motion  to  the  rod,   r,   which  oscillates  on  a  horizontal 

axis,  a.     To  this  axis  is  fixed  the  escapement,  PP,  terminated 

by  two    projections,    or  pallets  t   which 

work  alternately  in  the  teeth  of  the 

scape  ivheel,  S.     This  whee^   acted  on 

by  the  weight,   W,  through  a  train  of 

wheels  (not  shown  in  the  figure),  tends 

to  move  in  the  direction  of  the  arrow. 

If  the  pendulum  is  at  rest,  the  wheel 

is  held  at  rest  by  the  pallet,  P,  and 

with  it  all  of  the  clock  work. 

Now,  if  the  pendulum  be  moved  to 
the  position  shown  by  the  dotted  line, 
P  is  raised,  and  the  wheel  escapes  from 
the  pallet,  and  the  weight  causes  the 
wheel  to  turn  until  its  motion  is  ar- 
rested by  the  other  pallet,  P,  which 
has  been  brought  in  contact  with  another  tooth  of  the  wheel 
in  consequence  of  the  motion  of  the  pendulum.  In  this 
manner  the  descent  of  the  weight,  and  the  consequent  move- 
ment of  the  clock-work  is  regulated  by  the  pendulum.  The 
faces  of  the  pallets  are  slightly  inclined,  so  that  each  tooth 
of  the  wheel,  on  escaping,  gives  the  escapement  a  slight 
impulse,  which  is  communicated  to  the  pendulum,  and  com- 
pensates for  its  loss  of  motion,  due  to  friction  and  the  resist- 
ance of  the  air. 

105.   Since  the  length  of  the  seconds  pendulum  can 

be  determined  with  great  accuracy,  we  may  use  it  as  a 
means  of  determining  the  variation  in  the  intensity  of 
gravity  on  the  earth's  surface.  The  length  of  the  seconds 
pendulum  at  the  equator  is  39.02167  inches ;  at  New  York, 
39.10237  inches;  at  London,  39.13983  inches;  at  Spitzber- 
gen,  39.21614  inches.  The  same  pendulum  would,  there- 


PENDULUMS.  71 

fore,  vibrate  in  less  time  on  being  carried  from  the  equator 
to  the  poles.  Now,  as  the  fall  of  the  pendulum  is  due  to 
gravity,  the  lengths  of  any  two  pendulums  in  different  lati- 
tudes, which  have  the  same  time  of  vibration,  are  directly 
proportional  to  their  increments  of  gravity.  * 


*  The  time  of  vibration  of  a  pendulum  is  expressed  by  the  formula 
t  =  3.1416  y  I  -*-  g:  if  t  be  one  second,  then,  at  New  York,  g  =  9.87l.  or 
g  —  39. 10237X9.87  =385.94  inches.  The  fall  of  a  body  during  the 
first  second,  in  vacno  at  New  York,  is  one-half  this  quantity,  or  192.97 
inches. 

RECAPITULATION. 

The  pendulum  may  be  simple  or  compound. 

The  length  of  a  pendulum  is  the  distance  between  its  centers  of 
suspension  and  oscillation. 

The  time  of  one  vibration  depends, 

(1)  On  the  force  of  gravity. 

(2)  On  the  length  of  the  pendulum. 

(3)  It   is   not  sensibly  influenced  by  the   material  of  which  it  is 
made,  nor  by  the  arc   through  which   it  vibrates,   excepting  when 
these  arcs  are  very  unequal. 

PROBLEMS. 

1.  What  is  the   length  of  a  pendulum  making  one  vibration   in 
four   seconds?    In   one-fourth  of  a   second?    In   eight  seconds?    In 
one-eighth  of  a  second? 

2.  What  will  be  the  time  of  vibration  of  a  pendulum  thirteen  feet 
long?    Thirty  inches  long? 

3.  Suppose  a  seconds  pendulum  loses  one  minute  a  day,  should  it 
be  lengthened  or  shortened?    How  much  change  is  required? 

z 

y 


CHAPTER  VIII. 

SIMPLE   MACHINES. 

106.  A  machine  is  an  instrument  by  means  of  which  a 
force,  applied  at  a  certain  point,  tends  to  produce  motion  at 
another  point,  more  or  less  distant.     The  force  employed  in 
a  machine  is  called  the  power.     The  resistance  which  is  over- 
come by  a  machine  at   the  point  where  the  power  acts,  is 
called  the  weight  or  load. 

107.  Among  the  many  advantages   derived  from  the 
use  of  machines  are : 

(1)  They  enable  us  to  utilize  the  products  of  nature.     It 
is  the  knowledge   of  machinery  that   marks  civilized   life, 
since  by  it  we  have  mills  for  weaving  cloth,  grinding  flour, 
forging  iron,  etc. 

(2)  They  enable  us  to  employ  other  forces  than  our  own, 
as  the  strength  of  animals,  the  forces   of  wind,  water,  and 
steam. 

(3)  They  enatile  us  to  employ  our  full  strength  at  one 
time.     A  person  winding  thread  on  a  reel  expends  but  a 
small  portion  of  his  strength ;  with  suitable  machinery  he 
can  turn  many  reels  at  the  same  time. 

(4)  They  enable  us  to  change  the  direction  of  our  force. 
A  sailor  may  hoist  the  sails  of  a  ship  while  standing  on 
deck,  instead  of  pulling  them  up  after  he  has  climbed  the 
mast. 

(5)  They  enable  us  to  perform  work  that  we  could  not  do 
with  our  unassisted  strength.     By  using  a  crow-bar,  a  man 
may  raise  a  large  stone,  which  he  could  not  stir  with  his 
hands. 

(72) 


MACHINES.  73 

108.  No  machine  can   create  force.     It  is   merely  an 
inerff  instrument  for  the  advantageous  application  of  force. 
In  fact,  part  of  the  force  applied  to  machines  is  expended 
in  overcoming  friction,  the  resistance  of  the  air,  and  in  lift- 
ing the   parts  of  the  machine ;    hence,   only  a  part  of  the 
force  is  effective  in  doing  useful  work.     In  the   tJieoretical 
study  of  machines,  these  items  are  neglected,  and  it  is  gen- 
erally assumed  that  no  force  is  lost  in  the  machine. 

109.  The  work  of  the  power  is  equal  to  the  work  of  the 
load.    If  any  machine  enables  us  to  lift  a  weight  of  ten  pounds 
by  the  power  of  one  pound,  (1)  the  power  must  move  ten 
times  the  space  traversed  by  the  load ;  (2)  as  the  spaces  are 
traversed  in  the  same  time,  the  power  must  move  ten  times 
as  fast  as  the  load.     Conversely,  if  a  power  of  ten  pounds  is 
required  to  move  a  weight  of  one  pound,  (1)  the  load  will 
traverse  ten  times  the  space,  and  (2)  with  ten  times  the 
velocity  of  the  power.     The  law  of  virtual  velocities  is  an  ex- 
pression of  these  facts.     It  also  receives  a  concise  expression 
in  the  axioms, 

"What  is  gained  in  power  is  lost  in  velocity; 
What  is  gained  in  velocity  is  lost  in  power." 

110.  All  machinery  may  be  comprised  in  six  elementary 
forms,  called  simple  machines.     These  are  (1)  the  lever,  (2) 
the  wheel  and  axle,  (3)  the  pulley,  (4)  the  inclined  plane, 
(5)  the  wedge,    (6)  the  screw.     We  shall  study  only  the 
most  important  varieties  of  these. 

111.  A  lever  is  an  inflexible  bar,  moving  freely  about  a 
fixed  point,  Avhich  is  called  a  fulcrum.     The  arms  of  the 
lever  are  the  parts  into  which  the  fulcrum  divides  it. 

There  are  three  classes  of  levers  which  are  represented  in 

Fig.  43.     In  levers  of  the  first  kind,  the  fulcrum  is  between 

the  power  and  the  load.     In  levers  of  the  second  kind,  the 

load  is  between  the  power  and  the  fulcrum.     In  levers  of 

PHYS.  7. 


74 


ELEMENTS  OF  PHYSICS. 


the    third   kind,  the   power  is   between   the   load   and  the 
fulcrum. 


112.  Familiar  illustrations. 
A  crow-bar  is  a  lever  of  the 
first  kind  when  we  press  one 
end  downward  to  raise  a  load 
above  a  block  used  as  a  fulcrum, 
Fig.  44.  It  is  a  lever  of  the 
second  kind,  when  one  end  rests 
on  the  ground  as  a  fulcrum  and 
we  raise  the  other  end  upward 
to  lift  the  load,  Fig.  45.  A 
fishing  rod  is  a  lever  of  the 
third  kind ;  the  fish  being  the 


W 


W    F 


II 


71 


m 

FIG.  43. 

load,  the  power  is  applied  by  one  hand,  while  the  other  hand 
at  the  end  of  the  rod  acts  as  the  fulcrum.     The  hinges  of  a 


FIG.  44. 


FIG.  45. 


door  are  its  fulcra;  the  load  is  at  the  center  of  gravity  of 
the  door ;  in  closing  it,  it  is  a  lever  of  the  second  kind,  when 
the  hand  is  applied  near  the  latch ;  but  a  lever  of  the  third 
kind  when  the  hand  is  near  the  hinges. 

Since  the  work  of  the  power  is  equal  to  the  work  of  the 
load,  the  power  multiplied  by  the  vertical  distance  through 
which  it  passes  equals  the  load  multiplied  by  the  vertical  dis- 
tance through  which  it  passes.  This  law  applies  to  all 
machines,  but  we  can  give  it  another  expression,  of  greater 
convenience  for  each  simple  machine.  Thus : 

113.   The  law  of  the  lever.     The  product  of  the  power  inul- 


LEVEES.  75 

tiplied  by  its  distance  from  the  fulcrum  is  equal  to  the  product  of 
Hie  load  multiplied  by  its  distance  from  the  fulcrum. 

That  is,  using  the  letters  in  Fig.  43  : 

P  x  P~F=  L  X  "WF. 

This  law  is  called  a  statical  law,  because  it  expresses  the 
relation  of  the  power  to  the  load  when  a  machine  is  in  ex- 
act equilibrium.  To  produce  motion  it  is  necessary  that 
this  equilibrium  should  not  exist,  which  will  be  the  case 
when  one  product  exceeds  the  other.  The  machine  will 
then  move  in  the  direction  of  the  greater  product. 

Examples.  In  a  lever  of  the  first  kind,  sixteen  inches 
long,  with  the  fulcrum  four  inches  from  the  load,  and, 
therefore,  twelve  inches  from  the  power,  a  power  of  one 
pound  will  balance  a  load  of  three  pounds.  Now,  if  an 
ounce  be  added  to  the  power  it  will  raise  the  load ;  if  it  is 
added  to  the  load,  the  power  will  be  raised. 

In  a  lever  of  the  second  kind,  sixteen  inches  long,  with 
the  load  four  inches  from  the  fulcrum  and  the  power  six- 
teen inches,  a  power  of  one  pound  will  balance  a  load  of 
four  pounds. 

In  a  lever  of  the  third  kind,  sixteen  inches  long,  with  the 
power  four  inches  from  the  fulcrum,  a  power  of  four  pounds 
will  balance  a  load  of  one. 

If  we  wish  to  prove  these  by  actual  experiments,  we  must 
first  balance  the  lever  by  a  sufficient  counterpoise,  before 
attaching  the  power  and  the  load. 

114.  Levers  of  the  first  and  second  kinds  are  generally 
used  to  move  heavy  weights  with  small  powers.  Their  effi- 
ciency may  be  increased  (1)  by  increasing  the  power ;  (2)  by 
increasing  its  relative  distance  from  the  fulcrum.  Levers 
of  the  third  kind  are  used  when  we  wish  to  move  small  loads 
with  great  velocity  by  the  use  of  great  powers.  We  may 
also  employ  levers  of  the  first  kind  for  the  same  purpose. 


76 


ELEMENTS  OF  PHYSICS. 


115.  When  a  beam  rests  on  two  props  and  supports  a 
weight  between  them,  the  amount  supported  by  either  prop 
may  be  estimated  by 
considering  it  as  the 
power  and  the  other 
prop  as  the  fulcrum.  If 
A  and  B  carry  a  weight 
between  tlrem  on  a  pole, 
each  man  will  bear  half 
the  burden  if  the  weight 
hangs  from  the  middle 
of  the  pole.  In  all  other 
cases,  the  load  sustained 
by  each  increases  as  the  FIG.  46. 

distance  between  him  and  the  load  decreases.  For  example : 
if  the  weight  is  one-third  the  length  of  the  pole  from  A,  he 
will  bear  two-thirds  of  the  burden  and  B  one-third.  Two 
horses  attached  to  a  wagon  may  be  made  to  pull  unequal 
loads  by  placing  the  bolt  of  the  whipple-tree  nearer  the 

stronger  horse. 

116.  When  a  small  force 
is  required  to  sustain  a  consid- 
erable weight,  and  it  is  not 
convenient  to  use  a  long  lever,  a 
combination  of  levers,  called  a 
compound  lever,  may  be  em- 
ployed. 

A  compound  lever  is  shown 
in  Fig.  47.  A  F  is  a  lever  of 
the  second  kind;  the  power, 
P,  acting  at  A  produces  a 
FlG-  47-  downward  force  at  B  as  many 

times  greater  than  itself  as  the  distance  A  F  is  greater  than 


DANCES, 


B  F.  This  effect  is  then  transmitted  as  a  power  at  A't  which 
will  tend  to  raise  B'  upward,  with  a  force  as  many  times 
greater  than  itself  as  A'F'  is  greater  than  F'B'.  Finally, 
the  effect  at  B'  will  be  a  new  power  when  transmitted  to  A", 
and  will  tend  to  lift  the  load  at  B",  with  another  increase 
of  effect.  If  these  levers  are  so  arranged  that  the  power 
arm  in  each  is  ten  times  as  long  as  the  load  arm,  a  power 
of  one  pound  at  P  will  balance  a  load  of  10  X  10  X  10  = 
1,000  pounds  at  '  L. 

When  a  compound  lever  is  at  equilibrium,  the  power  multi- 
plied by  the  continued  product  of  the  alternate  arms,  commencing 
with  the  power,  equals  the  load  multiplied  by  tlie  continued  prod- 
uct of  the  alternate  arms,  commencing  with  the  load. 

117.  The  practical  applications  of  the  lever  are  very 
numerous.  The  balance  is  a  lever  of  the  first  kind,  having 
two  equal  arms.  Delicate  balances  have  a  small  needle  at- 


E 


FIG.  48. 

tached  to  the  center  of  motion,  which  oscillates  before  an 
index,  n,  to  show  very  small  deviations  of  the  beam. 

A  balance  is  sensitive,  when  a  very  small  difference  be- 


78  ELEMENTS  OF  PHYSICS. 

tween  the  weights  causes  a  perceptible  motion  in  the  pointer. 
It  must  be  in  a  state  of  stable  equilibrium;  that  is,  the 
center  of  gravity  should  be  below  the  fulcrum,  but  not  too 
far,  because  it  will  require  too  great  a  force  to  set  it  in 
motion.  The  apparatus  of  Fig.  31  well  illustrates  this ;  the 
horizontal  needle  will  be  the  most  sensitive  to  a  small  addi- 
tion of  weight,  when  the  vertical  needle  is  so  placed  that 
the  center  of  gravity  of  the  apparatus  is  a  very  little  below 
the  axis  of  suspension. 

The  arms  of  a  balance  must  be  equal  in  length,  otherwise 
one  will  have  a  greater  leverage  than  the  other,  and  un- 
equal weights  will  be  required  to  produce  equilibrium.  To 
test  this,  place  weights  in  each  scale  pan  and  bring  the 
beam  to  a  horizontal  position.  Now  transfer  the  weights  to 
the  opposite  scale  pans.  If  the  beam  remains  horizontal,  the 
arms  are  equal. 

118.  Dishonest   dealers   are  said   to  use  balances  with 
unequal  arms,  placing  their  merchandise  when  buying  in  the 
shorter  arm,    but   when    selling    in   the   longer.     The   true 
weight  of  the  merchandise  is  the  square  root  of  the  product 
of  the  false  weights.     That  is,  if  a  body  requires  nine  pounds 
to  balance  it  from  one  side  and  four  pounds  from  the  other, 
the  true  weight  is  six  pounds.* 

119.  The  wheel  and  axle  consists  of  a  wheel  and  cylin- 
der firmly  united  and   free  to  revolve  on  a  common  axis. 
The  power  is  applied  at  the  circumference  of  the  wheel  and 
tends  to  move  a  load  applied  at  the  circumference  of  the 
cylinder  or  axle.     This  machine  acts  continuously  as  a  lever 


#When  a  body  whose  true  weight  is  w  is  in  (7,  let  it  be  balanced 
by  a;  pounds  in  E.  When  in  E,  by  y  pounds  in  C,  and  let  A  and  B 
be  the  lengths  of  the  arms.  Then, 

ivA=xB  and  wE  —  yA.    Multiplying  these  together  wzAB  = 
Dividing  by  AB,  w^—xy.    w=\/xy. 


WHEEL  AND  AXLE. 


79 


FIG.  49. 


of  the  first  kind,  the  fulcrum  being  at  _F,  the  common  cen- 
ter, the  arms  of  the  lever  being  A  F  and  FB, 
the  radii  of  the  wheel  and  axle.  Hence,  the 
power  multiplied  by  the  radius  of  ilie  wheel  equals 
the  load  multiplied  by  the  radius  of  the  axle.  That 
is,  P  x  XF=  L  x  ^OT 

Example.  When  the  wheel  is  six  feet  in  ra- 
dius and  the  axle  six  inches,  a  power  of  one 
pound  will  balance  a  load  of  twelve  pounds. 

120.  In  the  various  forms  of  this  machine,  the  load  is 
generally  attached  to  a  rope  wound  round  the  axle;  the 
power  is  applied  in  several  different  ways. 

The  form  represented  in  Fig.  49  is  that  used  in  ware- 
houses, in  which  the  power  is  applied  by  means  of  a  rope 
coiled  on  the  wheel.  When  the  rope  on  the  wheel  is  un- 
wound, that  on  the 
axle  is  wound  up, 
and  the  load  raised. 
The  power  may  also 
be  applied  to  pins 
projecting  from  the 
wheel,  as  in  the  steer- 
in  g  apparatus  on 
large  vessels. 

It  is  not  necessary  that  the  power  be  applied  to  a  complete 
wheel,  since  a  single  spoke  will  answer. 
The  winch  of  the  common  windlass, 
Fig.  50,  is  such  a  spoke  for  the  appli- 
cation of  the  power.  In  the  windlass 
used  on  ships,  the  winch  is  replaced 
by  handspikes  which  fit  into  slots  cut  in  FIG.  51. 

the  axle,  and  are  shifted  as  occasion  requires.  The  capstan, 
Fig.  51,  is  a  vertical  windlass,  turned  by  men  walking  around 
it  and  pressing  against  handspikes  inserted  in  the  top  or  drum. 


FIG.  50. 


80 


ELEMENTS  OF  PHYSICS. 


121.    The  power  of  this  machine  may  be  augmented  on 
the  principle  of  the  compound  lever,  by  combining  several, 


FIG.  52. 

so  that  the  axle  of  the  first  may  act  on  the  wheel  of  the 
second,   and   so   on.      These    are    frequently   connected    by 


FIG.  53. 

means  of  cogs,   as   in  clock-work ;    or  by  means  of  endless 
bands  of  leather,  as  in  turning  lathes. 

122.    The  pulley.     Suppose  a  cord,  fastened  at  one  end 
to  a  hook,  supports  a  load  at  the  other  end.     The  tension 


THE  PULLEY. 


81 


of  the  cord  will  be  transmitted  throughout  its  whole  length, 
and  exert  a  force  on  the  hook  equal  to  the  weight  of  the 
load.  If  the  cord  be  passed  over  the  hook  and  one  end 
held  by  the  hand,  the  tension  of  the  cord  will  be  the  same, 
and  the  hand  must  exert  a  force  equal  to  the  load.  If  we 
pull  up  the  weight  by  the  hand,  we 
shall  gain  no  mechanical  advantage  ex- 
cept a  change  in  the  direction  in  which 
the  power  acts.  In  fact  there  will  be  a 
loss,  due  to  the  friction  of  the  cord  upon 
the  hook.  We  may  diminish  the  friction 
by  passing  the  cord  over  a  wheel  revolv- 
ing on  the  hook  as  its  axis,  but  can  not 
lessen  the  tension  of  the  cord.  A  pulley  FIG.  54. 

is  a  small  grooved  wheel  revolving  about  an  axis,  and  hav- 
ing a  cord  passing  over  its  circumference.  If  the  axis  is 
fixed,  the  pulley  is  a  fixed  pulley :  if  the  axis  is  movable,  the 
pulley  is  a  movable  pulley. 

123.  In  the  fixed  pulley  the  power  and  load  are  equal. 
The  advantage  derived  from  its  use  is  merely  a  change  in 
the  direction   of  the  power.     Thus,  if  a  fixed  pulley  be  at- 
tached  to   the   rafters  of  a  house,  a  man  standing  on  the 

ground  may  raise  loads  to  any  floor 
of  the  building.  As  it  is  easier 
for  him  to  pull  the  rope  down  than 
it  would  be  to  lift  the  weight  di- 
rectly upward,  he  can  also  afford  to 
overcome  the  friction  of  the  pulley. 
By  the  use  of  two  fixed  pulleys,  as 
in  Fig.  55,  horizontal  motion  may 
-  55'  be  converted  into  vertical. 

124.  Movable  pulley.    If  a  cord  be  fastened  at  each  end 
to  a  hook  and  a  load  hung  by  a  ring  in  the  middle  of  the 


82 


ELEMENTS  OF  PHYSICS. 


cord,  the  weight  of  the  load  will  be  distributed ;  that  is,  each 
half  of  the  cord  will  support  but  half 
the  load.  Therefore,  if  a  fixed  pul- 
ley take  the  place  of  one  of  the 
hooks,  the  power  required  to  support 
the  load  will  be  one-half  of  the 
weight  of  the  load.  If  it  is  desired  FIG.  56. 

to  elevate  the  load,  a  movable  pulley  may  be  substituted  for 
the  ring  in  order  to  have  less  friction,  as  in  Fig.  57. 

If  one  end  of  the  cord  be  attached  to  the  top 
of  the  movable  pulley,  as  in  Fig.  58,  the  tension 
due  to  the  load  will  be  distributed  in  three  equal 


FIG.  57. 


FIG.  58. 


FIG.  59. 


parts.  Consequently  the  tension  of  the  part  of  the  cord  to 
which  the  power  is  applied  will  be  one-third  of  the  load, 
and  the  combination  will  be  in  equilibrium  when  the  power 
is  one-third  of  the  load.  In  the  arrangement  of  Fig.  59, 
the  power  is  one-fourth  of  the  load. 

125.  As  fixed  pulleys  do  not  increase  the  power,  the 
gain  in  the  last  three  examples  must  be  due  to  the  distribution 
of  the  tension  among  the  parts  of  the  rope  supporting  the 
movable  pulley.  Hence,  the  load  equals  the  power  multiplied 


INCLINED  PLANE. 


83 


by  the  number  of  parts  of  the  cord  engaged  in  supporting  the 
movable  pulley.* 

126.  The  inclined  plane  is  a  hard,  smooth,  inflexible 
surface,  inclined  to  the  horizon.  When  a  load  is  placed  on 
a  horizontal  plane,  the  whole  weight  is  supported  by  the 
plane :  if  the  plane  is  tilted,  a  portion  of  its  weight  tends  to 
make  the  load  slide  or  roll  down  the  plane.  Thus  in  Figs.  60 


B  G  A 

FIG.  60. 

and  61,  the  weight  of  the  load  lies  in  the  direction  of  gravity, 
L  G :  this  may  be  resolved  into  two  components,  one,  L  N, 
pressing  upon  the  plane  and  perpendicular  to  it ;  the  other, 
L  E,  which  must  be  counterbalanced  by  the  application  of 
power,  to  prevent  the  load  from  sliding  down  the  plane. 
The  steeper  the  plane,  the  greater  will  be  the  power  required. 
We  shall  consider  two  cases. 

(1)  When  the  power  acts  parallel  with  the  plane,  as  in 
Fig.  60,  L  E  represents  the  power  required,  and  L  G,  or  its 
equal,  EN,  the  weight  of  the  load.  The  triangles,  LEN 
and  A  B  C,  are  similar,  and  L  E  will  bear  the  same  relation 
to  E  N  that  B  C  does  to  A  C;  that  is 

Power  is  to  load  : :  L  E  :  EN,  or  : :  B  C  to  A  C. 

Hence:  the  power  equals  the  load  multiplied  by  the  ratio  of  the 
vertical  height  of  iJie  plane  to  its  length. 

Thus,  the  power  required  to  keep  a  barrel  weighing  two 


*  The  law  supposes  that  there  is  but  one  cord,  and  that  its  parts 
are  parallel  to  each  other. 


84 


ELEMENTS  OF  PHYSICS. 


hundred  pounds  on  a  plank  twelve  feet  long,  with  one  end 
on  the  ground  and  the  other  on  a  wagon  three  feet  high, 
will  be  200  X  tV  =  50  pounds. 

This  is  the  most  advantageous  way  of  applying  the  power, 
because  its  whole  effect  is  expended  in  raising  the  load. 

(2)  When  the  power  acts  parallel  with  the  base,  as  in 
Fig.  61,  a  part  of  the  power  is  expended  in  increasing  the 
pressure  on  the  plane,  and  we  shall  find, 

Power  is  to  load  ::  LE  :  EN,  or  ::  B  C  :  AB. 
Hence:  the  power  equals  tfie  load  multiplied  by  the  ratio  of  the 
vertical  height  of  the  plane  to  its  base. 

127.  Familiar  examples  are  found  in  roads,  which  are 
seldom  perfectly  level.     On  a  level  road,   the  power  of  a 
horse  drawing  a  wagon  is  expended  in  overcoming  friction. 
On  a  road  rising  one  foot  in  twenty,  the  horse  must  lift 
one-twentieth  of  the  load  besides  overcoming  the  friction. 
If  we  reckon  friction  at  one-eighteenth  of  the  weight  of  the 
wagon  and  its  contents,  the  power  necessary  (^  -j-  y§-)  will 
be  almost  double  that  required  on  a  level  road.     Hence,  in 
ascending  mountains  the  road  winds  about  so  as  to  increase 
the  length  of  the  incline. 

128.  The  wedge  is  a  movable  inclined  plane.     If,  instead 
of  moving  the  weight  along  the  inclined  plane,  Fig.  61,  the 
plane  had  been  pushed  under  the  load,  the  same  advantage 
would  have  been  gained.     Therefore,  since 

in  the  wedge,  the  power  is  always  exerted 
parallel  to  the  base,  the  power  is  to  the  load 
as  the  height  of  the  wedge  is  to  tfie  base. 

129.  The  double  wedge,  as  Ac  A',  is  the 
form  generally  used.     As  each  face  meets 
half  the  resistance,  the  power  is  to  the  re- 
sistance as  half  the  thickness  of  the  wedge 
is  to  its  length,  jB  c. 


THE  SCREW.  85 

This  law  is  of  little  practical  use,  beyond  the  general  de- 
duction that  the  efficiency  of  the  power  increases  with  the 
thinness  of  the  wedge ;  because, 

(1)  The  power  is  applied,  not  by  a  continuous  force  or 
pressure,  but  by  percussion,  and  in  such  a  form  that  we  can 
not  give  it  a  numerical  value. 

(2)  The    surfaces    to    be   separated    generally  assist    the 
action  of  the  wedge,  by  their  elasticity  at  the  moment  of 
impact,  and  sometimes  by  the  leverage  of  the  faces  to  the 
cleft. 

(3)  The  value  of  the  wedge  is  often  entirely  dependent 
on  friction,  as  is  the  case  with  nails,  and  the  key-stones  of 
arches. 

130.  The  wedge  is  used  where  very  great  force  is  to  be 
exerted  through  a  small  space.     Masses  of  stone  and  timber 
are  cleft  by  wedges.     Ships  are  raised  when  on  the  stocks 
by  wedges  driven  under  their  keels.     Knives,  awls,  hatchets, 
chisels,  and  other  cutting  instruments,  are  wedges. 

131.  The  screw  is  another  variety  of  the  inclined  plane, 
as  may  be  shown  by  winding  a  triangular  piece  of  paper 
around  a  cylinder.     The  hypotenuse  will  form  a  spiral  path 
exactly  resembling  the  thread  of  a 

screw.  The  vertical  distance,  as  be, 
between  two  threads  represents  the 
height  of  the  plane,  and  the  circum- 
ference of  the  cylinder  the  base  of 
the  plane.  The  power  acts  parallel 
to  the  base,  as  in  the  second  case  of  FIG.  GS. 

the  inclined  plane.     Hence, 

The  poiver  is  to  tJie  load  as  the  vertical  distance  between  two 
adjoining  threads  is  to  Hie  circumference  of  the  screw. 

132.  In  actual  practice,  the  screw  consists  of  two  parts. 


86 


ELEMENTS   OF  PHYSICS. 


(1)  a  convex  grooved  cylinder,  or  screw,  S,  which,  turns 
within  (2)  a  hollow  cylinder  or  nut,  N,  whose  concave  sur- 
face is  cut  with  a  thread  exactly 
corresponding  to  the  threads  of 
the  screw.  The  power  is  em- 
ployed either  to  turn  the  screw 
within  an  immovable  nut,  or  to 
turn  the  nut  about  a  fixed  screw. 
In  both  cases,  it  is  generally  ap- 
plied by  means  of  a  lever.  This 
renders  the  contrivance  a  com- 
pound machine,  whose  advantage  may  be  found  by  the  fol- 
lowing law : 

The  poiver  is  to  the  load  as  the  vertical  distance  between  two 
adjoining  threads  is  to  the  circumference  described  by  the  power. 
Power  is  to  load  ::  be  :  2-  FP,  or  ::  be  :  6.2832  FT7 
Example.     If  the  threads  of  the  screw  are  one  inch  apart, 
and  the  lever  is  four  feet  long,  a  power  of  five  pounds  will 
exert   a   pressure   of    4  X  12  X  2  X  3.1416  X  5  =  1507.97 
pounds. 

133.   The  screw  is  used  for  compressing  cotton  and  hay, 

for  expressing  the 
juices  of  plants  and 
fruits,  for  raising 
buildings,  for  propel- 
ing  ships,  and  for 
many  minor  pur- 
poses. 

134.    Compound 
machines  are  combi- 
FIG.  65.  nations  of  two  or  more 

simple  machines.     One  of  the  most  useful  of  these  is  the 
endless  screw,  Fig.  65;  its  thread  works  obliquely  into  the 


HUMAN  MECHANISM. 


87 


E 


teeth  of  a  wheel,  which  supplies  the  place  of  the  nut. 
Cranes  and  derricks  are  combinations  of  pulleys  with  the  wheel 
and  axle.  The  crane  shown  in 
Fig.  66  has  a  wheel  and  axle  at 
G,  two  fixed  pulleys,  F  and  E, 
and  one  movable  pulley,  P.  The 
mechanical  advantage  of  a  com- 
pound machine  is  found  by  esti- 
mating the  effect  of  the  parts 
separately  and  then  multiplying 
these  together. 

135.  The  human  mechanism 
exhibits  many  examples  of  sim- 
ple machines.  FlG<  66< 

Thus,  the  nodding  of  the  head  illustrates  a  lever  of  the 
first  kind,  in  which  the  load  is  the  weight  of  the  head;  the 
fulcrum,  the  atlas  bone;  and  the  muscles  of  the  neck,  the 
power.  When  a  man  stands  on  his  toes,  the  floor  is  the 
fulcrum;  the  power  is  applied  at  the  heel  by  the  tendon 
Achilles;  and  the  weight  of  the  body  falls  between  the  ful- 
crum and  the  power.  This  is  a  lever  of  the  second  kind. 

We  employ  a  lever 
of  the  third  kind  in 
raising  the  fore-arm. 
The  hand,  and  any 
thing  that  it  contains, 
is  the  weight;  the  el- 
FIG.  67.  bow-joint,  the  ful- 

crum ;  and  the  power  is  applied-  by  a  muscle  attached  to  the 
fore-arm  a  little  in  front  of  the  joint,  Fig.  67.  In  biting  by 
the  front  teeth,  we  employ  a  lever  of  the  third  kind.  The 
force  exerted  by  the  muscles  which  raise  the  lower  jaw  is 
enormous.  In  man  it  can  not  be  less  than  three  hundred 


88  ELEMENTS  OF  PHYSICS. 

pounds,  and  in  the  tiger  it  must  exceed  two  thousand 
pounds.  The  muscle  which  directs  the  eye  downward  and 
inward,  passes  through  a  cartilaginous  pulley  attached  to  the 
frontal  bone.  Some  of  the  teeth  are  wedges,  capable  of 
cutting  like  chisels. 

Throughout  the  entire  frame  we  have  surprising  examples 
of  economy  of  material  to  the  end  designed;  combining 
lightness,  force,  firmness,  elasticity,  leverage,  motion,  resist- 
ance, security,  and  grace.  These  contrivances  are  so  numer- 
ous, and  so  wonderfully  constructed,  that  a  volume  would  be 
insufficient  to  describe  them. 

RECAPITULATION. 

Machines  are  simple  or  compound. 

f  Lever, 

)1.  Leverage,  j  Wheel  and  axle 

2.  Tension  of  ropes,  Pulley. 

C  Inclined  plane, 
3.  Inclined  surfaces,  <  Wedge, 


(_  Screw.* 
me  sirt^ 

the  compound  -lever  ;  (2)  by  uniting  two  or  mere  simple  machines, 

^ 


_  Screw.*    ft 
Machines  are  compounded  (1)  by  repeating  the  same  sirt^l^niachine, 


<r 


PROBLEMS. 


1.  Suppose  a  power  of  50  pounds  moves  through  a  vertical   dis- 
tance of   10  feet,  ho\/  high  can  it  lift  a  load  of  250  pounds?    How 
great  a  load  can  it  lift  100  feet  high  ?    In  each  case  what  will  be  the 
relative  velocities  of  the  power  and  the  load? 

2.  A  power  of  75  pounds  is  applied  at  one  end  of  a  lever  12  feet 
long  to  move  a  load  at  the  other  end;   what  will  be  the  load  when 
the  fulcrum  is  at  the  center  of  the  lever?    When   the  fulcrum  is  3 
feet  from  the  load?    1  foot  from  the  load? 

3.  When  the  same  bar  is  employed  as  a  lever  of  the  second  kind, 
what  will  be  the  load  when  it  is  sustained  at  the  center?    At  3  feet 
from  the  fulcrum?    At  1  foot? 


V 

PROBLEMS.  89 


4. 


L  If,  with  the  same  bar,  the  load  and  the  fulcrum  be  placed  at 
the  ends  and  the  power  applied  between  them,  what  will  be  the  load 
when  the  power  is  at  the  center?  At  3  feet  from  the  fulcrum?  At 
1  foot? 

5.  If,  with  the  same  bar,  a  power  of  80  pounds  balances  a  load  of  180 
pounds,  how  far  from  the  load  will  the  fulcrum  be  when  it  is  used 
as  a  lever  of  the  first  kind?    As  a  lever  of  the  second  kind? 

6.  If   A  and   B  carry  between  them,  on  a  pole  9  feet  long,  a  load 
of  150  pounds,  how  much  will  A  bear  when   the  load  is  3  feet  from 
him?    6  feet? 

7.  In    the  compound   lever,  shown  in    Fig.  47,  A  F  is  6  feet  long, 
A'  B'  4  feet,  A"  F"  5  feet,  and  the  distances  FB,  F'  B1,  F"  B",  each 
1  foot,  what  is  the  relation  between  the  power  and  the  load?    What 
load  may  be  sustained  by  a  power  of  60  pounds? 

8.  In  a  false  balance,  a  bundle  weighs  16  pounds  in  one  scale  pan 
and  9  pounds  in  the  other,  what  is  the   true  weight?    What  is  the 
relative  length  of  the  arms?    Prove  the  answers  obtained. 

9.  In  a  wheel  and  axle,  the  radius  of  the  wheel  is  10  feet  and  that 
of  the  axle  6  inches;  required,  the  load  that  may  be  sustained  by  a 
power  of  1  pound?    By  100  pounds? 

10.  With  the  same  machine,  what  will  be  the  length  of  the  rope 
unwound  from  the  wheel,  when  the  load  has  been  lifted  10  feet? 

11.  A  capstan  has  an  axle  one  foot  in  diameter,  and  is  furnished 
with  5  handspikes,  each  6  feet  long;  how  much  power  must  be  ap- 
plied at  each  handspike  to  lift  an  anchor  weighing  4,000  pounds? 

12.  In  a  wheel  and  axle,  the  axle  is  8  inches  in  diameter,  and  is 
turned  by  a  winch  of  2  feet  radius ;   what  is  the  load  that  may  be 
lifted  by  a  power  of  100  pounds?    What  is  the  power  required  for 
100  pounds? 

13.  In  a  train  of  3  wheels,  the  number  of  teeth   in  each  wheel  is 
64,  the    number  of   leaves  on    each  pinion  16:    when  a  power  of  10 
pounds  is  applied  at  the  circumference  of  the  first  wheel,  what  load 
will  be  sustained  at  the  third    pinion?    How  many  times  must  the 
first  wheel  revolve  in  order  that  the  third  pinion  be  turned  around 
once? 

14.  In  a  system  of  2  movable  pulleys,  with  a  continuous  cord,  the 
power  is  100  pounds ;  required,  the  load. 

PHYS.  8. 


90  ELEMENTS  OF  PHYSICS. 

15.  On  a  road  rising  1  foot  in  25,  what  power  will  be  required  to 
sustain  a  wagon  weighing  1,000  pounds? 

16.  In  a  book-binder's  press,  the  lever  is  6  feet  long,  and  the  threads 
of  the  screw  0.5  inch  apart ;  what  pressure  may  be  applied  by  a  power 
of  100  pounds? 

17.  If  12  turns  of  a  screw  carry  the  head   forward  1   inch,  what 
power,  applied  to  a  lever  6  feet  long,  is  required  to  exert  a  pressure 
of  2000  pounds? 

18.  In  the   crane,  Fig.  66,  the  axle   at  G   is  6   inches  in  diameter, 
and  the  winch  3  feet  in  radius,  with  one  movable  pulley ;  what  will 
be  the  relation   between  the  power  and   the  load?    The  wheel  and 
axle  remaining  the  same,  what  advantage  may  be  gained  by  the  use 
of  a  system  containing  four  movable  pulleys? 


CHAPTER  IX. 

FLUIDS   AT   REST. 

136.  Solids  act  in  masses ;  if  we  move  one  end  of  a  stick 
the  whole  stick  will  be  moved,  by  reason  of  the  coherence 
of  its  molecules.     The  molecules  of  fluids  act  independently 
of  each  other,  and  hence  will  move  on  the  application  of  a 
very  small  force. 

137.  Liquids  and  gases  are  governed  by  very  nearly 
the  same  laws.     The  principal  difference  between  them  arises 
from   the  fact  that  gases  are  easily  reduced  in  volume  by 
pressure,  while  liquids  may  be  considered  as  non-compressible 
fluids.     The  pressure  of  one  atmosphere  causes  in  water  a 
decrease  of  only  0.00005  part  of  its  original  volume,  and  in 
mercury  only  0.000005  part.     As  soon  as  the  pressure   is 
removed   both    liquids   and    gases   return   to   their,  original 
volume,   showing  that  they  are  both  perfectly  elastic.     The 
energy  of  the  elasticity  with  which  they  resist  a  force  that 
compresses  them  is  exactly  equal  to  the  compressing  force. 

\  138.  Solids  transmit  pressure  only 
in  the  direction  of  the  force  acting 
upon  them.  Liquids  transmit  pressure 
undiminished  in  every  direction^  This  fact 
may  be  demonstrated  by  experiment. 
Take  a  vessel  of  any  shape,  in  whose 
sides  are  cylindrical  apertures  closed 
by  movable  pistons,  whose  areas  are, 
respectively,  1,  2,  3,  4,  and  5  square  FIG.  cs. 

inches,   and  till    the   vessel   with  water  so  that  it  shall  be 

(01) 


92  ELEMENTS  OF  PHYSICS. 

completely  closed  in  on  all  sides.  Suppose  the  water  to 
have  no  weight  and  the  pistons  no  friction,  or,  what  amounts 
to  the  same  thing,  suppose  the  friction  is  equal  to  the 
weight  of  the  water,  then  there  will  be  no  tendency  to 
motion  anywhere  in  the  vessel.  Now  apply  a  pressure  of 
one  pound  upon  the  piston  whose  area  is  one  square  inch. 
Each  molecule  beneath  the  piston  will  be  slightly  com- 
pressed, and  develop  a  corresponding  elastic  force  in  each. 
Each  one  will  then  react  upward  against  the  piston,  down- 
ward against  the  molecules  beneath,  and  sideways  against 
the  adjoining  molecules,  or  against  the  sides  of  the  vessel. 
The  next  tier  of  molecules  will  transmit  the  pressure  in  the 
same  way  to  a  third  tier,  and  they  onward,  until  every 
molecule  both  receives  and  transmits  an  equal  pressure. 
Therefore,  each  piston  will  be  thrust  outward  with  a  force 
proportional  to  the  number  of  molecules  beneath  it,  and,  as 
these  are  of  the  same  size,  the  pressure  on  each  piston  will 
be  proportional  to  its  area.  It  will  require  a  pressure  of 
two  pounds  to  keep  a  piston  of  two  square  inches  in  place; 
three  pounds  for  one  of  three  square  inches,  etc.  Any  por- 
tion of  the  sides  of  the  vessel,  or  of  any  solid  immersed  in 
the  fluid,  will,  in  like  manner,  sustain  a  pressure  in  propor- 
tion to  its  area. 

139.  A  liquid  is  not  at  rest  unless  its  molecules  are 
somehow  restrained  by  a  vessel  or  its  equivalent.  In  an 
open  vessel,  the  force  of  gravity  tends  to  bring  each  mole- 
cule as  near  the  earth's  center  as  possible.  ^  J|f 
This  will  only  be  the  case  when  the  sur- 
face is  perpendicular  to  the  force  of  gravity ; 
for  suppose  the  surface  Avere  curved,  as  in  FIG.  09. 

Fig.  69,  then  a  particle  at  M  would  exert  a  pressure  by 
reason  of  its  weight.  This  would  be  transmitted  downward 
and  sideways;  but,  as  there  would  be  no  equal  pressure  be- 


WATER  LEVEL.  93 

low  A  to  counterbalance  it,  a  part  of  its  pressure  would  pro- 
duce motion  in  the  fluid,  and  would  finally  bring  the  surface 
to  the  common  level,  AB.  ^ 

140.  As    two    verticals,   near    each    other,    are    sensibly 
parallel,   any  liquid   surface   between   them   is   level  or  hori- 
zontal.    As  two   verticals,   drawn    at    distant    points,    incline 
toward  each  other,  large  surfaces  of  liquids  are  curved  so  as 
to  correspond  with  the  general  form  of  the  earth's  surface.* 

141.  Water  always  seeks  its  lowest  level.     It  is  on 
this  principle  that  water  is  conveyed  from  reservoirs  through 
pipes   to  supply  cities.     The  water  rises  in  the  pipes  to  the 
exact  level  of  the  reservoir ;    and  would  rise  to  the  same 
level  in  fountains,  were  it  not  for  the  resistance  of  the  air, 
and  other  impediments  to  motion.     The  spirit  level,  which 
is  used  to  determine  horizontal  lines,  operates  on  the  same 
principle. 

This  consists  of  a 
closed     glass     tube, 

slightly  curved,  and  ^ 

6      J  FIG.  70. 

nearly     filled     with 

some  liquid  not  easily  frozen.  The  tube  is  then  so  placed 
in  a  brass  case  that  when  the  apparatus  is  perfectly  hori- 
zontal, the  small  bubble  of  air,  B,  will  lie  exactly  at  the 
highest  point. 

142.  Fluids  exert  pressure  in  consequence  of  gravity. 
Suppose  the  vessels,  A  B  CD,  to  be  filled  with  any  liquid  to 
the  same  level,  CD,  and  consider  each  divided  into  an  infi- 
nite number  of  horizontal  strata,  as  indicated  bv  the  lines 


#The  amount  of  curvature   increases  with    the  square  of  the  dis- 
tance, as  shown  by  the  following  tahle : 

Distance  in  miles 12345678"910 

Curvature  in  feet 6G3  2.65  5.97  10.6  1G.6  23.9  32.5  42.4  53.6  66.3, 


94 


ELEMENTS  OF  PHYSICS. 


FIG.  71. 


of  the  diagram.  Each  stratum  may  then  be  considered  as 
a  cylinder  exerting  a  pressure  on  its  base  equal  to  its  own 
weight.  By  the  law  of 
fluid  pressures,  the  weight  ^||  |p  (?[ 
of  each  stratum  above 
will  be  transmitted  undi- 
minishcd  to  each  stratum 
below  in  the  ratio  of  their 
areas;  therefore,  the  press- 
ure sustained  by  any  sec- 
tion, as  A  B,  G  L,  G  E,  will  be  equal  to  the  weight  of  a 
column  of  the  liquid  whose  base  equals  the  area  of  the 
section,  and  whose  height  equals  its  depth. 

143.  The  pressure  exerted  by  a  fluid  is  proportional 
to  its  depth.  (1)  The  downward  pressure  of  liquids  may  be 
illustrated  by  tying  a  piece  of  sheet  rubber  over  one  end  of 
a  long  open  tube.  On  pouring  water  into  the  tube  the  rub- 
ber will  be  distended  in  proportion  to  the  depth  ojf  the 
water.  (2)  The  upward  pressure  of  liquids  is  easily  shown 
by  thrusting  the  closed  end  of  the 
tube  into  water,  when  the  rubber 
will  be  driven  into  the  tube  further 
and  further  as  the  depth  increases. 
It  is  generally  demonstrated  by  tak- 
ing an  open  tube,  having  disks  of 
lead  or  leather  closely  fitting  the  lower 
end.  Support  the  disk  by  a  thread 
until  the  tube  is  plunged  in  a  vessel 
of  water.  The  disk  will  then  be  re- 
tained in  its  place  by  the  upward 
pressure.  If,  now,  the  tube  be  care- 
fully filled,  the  disk  will  not  fall  off  until  the  weight  of  the  in- 
terior column  plus  that  of  the  disk  exceeds  the  weight  of  the 


FIG.  72. 


PASCAL'S  EXPERIMENT. 


exterior  column.  (3)  The  lateral  pressure  of  liquids  is  shown 
by  the  velocity  with  which  they  flow  from  orifices  at  differ- 
ent depths.  A  fine  illustration  is  represented  in  Fig.  73. 
It  consists  of  a  tall  jar  with  a 
stop-cock  near  the  base,  and  made 
to  float  on  the  surface  of  some 
liquid.  If  the  jar  be  filled  with 
water  and  the  stop-cock  closed, 
the  lateral  pressure  at  L  and  U 
will  be  equal.  Hence,  the  jar 
will  remain  at  rest,  because  the 
pressures  are  equal ;  but  on  open- 
ing the  cock,  the  FIG.  73. 
pressure  at  L  is  removed,  and  the  lateral 
pressure  at  L'  will  be  effective  in  driving  the 
float  in  the  direction  of  the  arrow,  and  op- 
posite to  the  course"  of  the  stream. 

144.  The  pressure  is  independent  of  the 
quantity  of  the  liquid.  In  1647,  Pascal 
fitted  to  the  upper  head  of  a  small  cask 
a  tube  about  forty  feet  long.  The  cask 
being  filled  with  water,  he  succeeded  in 
bursting  it  by  filling  the  tube.  As  an  ounce 
of  water  will  fill  a  tube  forty  feet  long  and 
y1-  of  an  inch  in  diameter,  an  ounce  would 
have  sufficed ;  for  a  tube  T1^  of  an  inch  in 
diameter  has  an  area  of  only  ^yj-of  a  square 
inch,  so  that  the  ounce  weight  would  mul- 
tiply itself  two  hundred  and  seventy-seven 
times  for  each  square  inch  on  the  vessel, 
FIG.  74.  which  becomes  a  pressure  of  17.31  pounds 
for  each  square  inch.  Either  head  of  an  eight  gallon  cask 
would  have  to  sustain  a  pressure  of  about  two  thousand 


96  ELEMENTS  OF  PHYSICS. 

five   hundred   pounds,   and  the   total  pressure  on   the  cask 
would  have  exceeded  fifteen  thousand  pounds. 

145.  As  fluid  pressure  is  transmitted  un- 
diminished  in  all  directions,  it  will  not  be  af- 
fected by  bends  in  the  tube.     The  hydrostatic 
bellows  consists  of  two  boards,  A  B,  united  by 
stout  leather,  and  a  small  tube,  c,  communi- 
cating with  the  interior.     Water  poured  into 
the  tube  will  lift  the  upper  board,  with  a  force 
proportioned  to  the  height  of  water  in  the 
tube.     Each  foot  in  height  represents  a  press- 
ure of  0.4335  pounds   to    the  square    inch; 
therefore,  if  the  upper  board  has  an  area  of  ^ 
one  hundred  square  inches,  and  the  height  of  B 
the  tube  is  three  feet,  the  weight  capable  of 

being  supported   on  A  will  be  .4335  X  100  X  3  =  130.05 
pounds. 

146.  If  A  had  been  made  to  rise  toward   an  immovable 
bar  placed  above  it,  any  substance  between   the  board  and 
the  bar  would  have  been  compressed  with  the  force  of  43.35 
pounds  for   every  foot  in   the  height  of  the  tube.     By  in- 
creasing the  length  of  the  tube,  the  pressure  will  soon  be- 
come great  enough  to  rupture  the  bellows.     The  same  effect 
may  be  produced,  if,  instead  of  lengthening  the  tube,  a  piston 
is  employed  to  force  water  down  the  tube.     By  the  law  of  fluid 
pressures,  a  pressure  equal  to  that  upon  the  piston  would  be 
communicated  to  each  equal  area  in  the  bellows. 

147.  Bramah's  hydraulic  press  is  constructed  on  this 
principle. 

Within  the  collar  of  the  iron  cylinder,  B,  a  cast-iron 
ram,  P,  works  water-tight.  The  substance  to  be  pressed  is 
placed  between  the  ram,  P,  and  the  immovable  plate,  Q. 
Water  is  brought  by  a  force-pump  into  the  small  cylinder, 


THE  HYDRAULIC  PRESS. 


97 


A,  and  is  thence  driven  by  the  piston,  r,  through  the  tube, 
K,  into  the  larger  cylinder.  The  advantage  gained  will  be 
in  proportion  to  the  areas  of  the  two  cylinders.  If  the  large 
cylinder  is  one  hundred  times  the  area  of  the  small  cylinder, 


FIG.  76. 

one  pound  applied  at  the  piston  will  produce  a  pressure  of 
one  hundred  pounds  on  the  ram.  The  efficiency  of  the 
press  is  further  increased  by  the  handle,  M,  a  lever  of  the 
second  class.  If  the  distance  from  the  fulcrum  to  the  applied 
force  is  ten  times  the  distance*  to  the  weight,  a  power  of  one 
hundred  pounds  will  transmit  one  thousand  pounds  to  the 
piston,  and  tend  to  raise  the  ram  by  a  force  of  one  hundred 
thousand  pounds. 

148.   In  this  press  very  little  power  is  lost  by  friction, 
and,   practically,   the  advantage  gained   is  limited  only  by 
PHYS.  9. 


98 


ELEMENTS  OF  PHYSICS. 


the  strength  of  the  materials.  Like  all  other  machines,  it 
is  governed  by  the  law  of  virtual  velocities,  and  works  very 
slowly.  In  the  example  supposed,  one  hundred  parts  of 
water  driven  out  of  the  small  cylinder  would  raise  the  ram 
but  one  part.  The  hydraulic  press  is  used  wherever  great 
power  is  to  be  transmitted  through  small  space,  as  in  ex- 
tracting oils  from  seeds  and  crude  fats,  and  in  pressing 
cotton  for  shipment.  Two  of  these  machines  were  employed 
to  raise  the  immense  tubes  of  the  Britannia  Bridge  to  their 
proper  elevation.  Such  was  the  force  employed  to  drive 
the  water  into  the  cylinder,  that  it  was  sufficient  to  raise  a 
jet  twenty  thousand  feet  high,  or  over  the  peak  of  Chimbo- 
razo.  With  such  pressures,  the  weight  of  the  water  in  the 
smaller  cylinder  becomes  inconsiderable. 

149.  Trhe  pressure  is  proportional  to  the  density  of  the 
fluid.  If  mercury  be  poured  into  a  U  tube,  so  as  just  to 
fill  the  bend,  and  then  water  be  poured  into 
one  arm  of  the  tube,  the  mercury  will  be 
driven  a  little  way  into  the  other  arm.  Now, 
if  we  measure  the  height  of  the  mercurial 
column  above  the  lowest  level  of  the  water 
(represented  in  the  figure  by  the  dotted  line), 
we  shall  find  that  it  is  y^g  as  high  as  the  col- 
umn of  water. 

150.  Principle  of  FlG-  77- 
flotation.  Suppose  a  solid,  ABGDy 
to  be  immersed  in  water,  every  por- 
tion of  fts  surface  will  undergo  press- 
ure. The  horizontal  pressures,  on  the 
sides  of  the  body,  will  all  be  equal  and 
opposite,  and  have  no  tendency  to 
FlG-  "8-  move  the  body  in  any  direction.  The 

upper  face  will  be  pressed  downward  by  a  liquid  column, 


PRINCIPLE  OF  ARCHIMEDES.  99 

MABN,  the  lower  face  will  be  pressed  upward  by  the 
liquid  column,  M  CD  N.  The  solid  will,  consequently,  be 
urged  upward  by  a  pressure  which  equals  the  difference  of 
these  columns;  MCD N—  M ABN=  A  B  CD.  This  is 
equal  to  the  weight  of  a  volume  of  the  fluid  equal  to  the 
volume  of  the  solid. 

Now,  as  the  force  of  gravity  tends  to  bring  the  body 
lower,  and  as  the  upward  pressure  of  the  fluid  tends  to 
raise  it,  the  effect  will  be  to  lessen  the  apparent  weight  of 
the  body.  (T)  A  rare  body,  like  cork,  will  rise  to  the  sur- 
face, and  finally  displace  a  volume  of  the  fluid  equal  to  its 
own  weight.  If  attached  to  a  balance  it  will  exert  no  pull, 
and  may  be  said  to  have  lost  all  its  weight.  (2)  A  dense 
body  will  tend  to  sink  deeper  in  the  fluid,  but  if  this  is  re- 
sisted by  a  string,  the  pull  will  be  less  than  its  whole  weight 
by  the  weight  of  the  volume  of  the  fluid  displaced ;  that  is, 
by  the\weight  of  a  volume  equal  to  its  own  bulk.  \ 

151.  This  principle  was  discovered  by  Archimedes,  about 
230,  B.  C.     It  may  be  verified  by  hanging  to  one  arm  of  a 
balance  a  cup,  A,  and  a  solid  cylinder,  B, 

which  exactly  fits  within  the  cup.  Having 
first  counterpoised  the  balance  by  weights 
put  in  the  other  scale  pan,  immerse  the  solid, 
B,  in  water.  The  equilibrium  will  be  de- 
stroyed, because  the  solid  loses  a  portion  of 
its  weight,  but  will  be  restored  when  the  cup, 
A,  is  filled  with  water. 

Therefore,  a  solid  immersed  in  a  fluid  loses 
an  amount  of  weight  equal  to  the  weight  of  an 
equal  volume  of  the  fluid. 

152.  We  can  now  understand  how  the 

specific  gravity  of  solids  is  found  (read  pages  13  and  14). 


100  ELEMENTS  OF  PHYSICS. 

We  first  weigh  the  body  in  air,  then  suspend  it  by  a  hair 
and  weigh  it  in  water.  The  difference  of  the  two  weights  is 
the  weight  of  an  equal  volume  of  water.  Hence, 

Weight  of  given  substance  in  air        ~      ... 

-^-f—^7 =-77^ —  — —  Specific  gravity. 

Loss  of  weight  in  water 

Thus,  a  mass  of  lead,  weighing  a  pound  in  air,  weighs 
14.6  ounces  in  water.  Its  specific  gravity  is,  therefore, 
16  -r-(16  — 14.6)  =  11.4. 

153.  When  a  solid  is  lighter  than  water,  it  is  neces- 
sary to  submerge  it  by  attaching  to  it  a  heavy  mass,  whose 
weight  in  water  and  in   air  are  known.     The  loss  of  the 
combined  bodies  is  evidently  the  weight  of  water  equal  to 
their  united  volume.     If  the  loss  sustained   by  the  heavy 
body  alone  is  taken  from  this,  the  remainder  will  be  the 
weight  of  water  equal   to  the  volume  of  the  light  body. 
The  weight  of  the  light  body  in  air  divided  by  this  remain- 
der, will  give  its  specific  gravity. 

Thus,  attach  to  a  pound  of  lead  two  ounces  of  cork.  The 
weight  in  water  is  8.6  ounces.  The  loss  of  both  bodies  is 
16  -f-  2  —  8.6  =  9.4,  but,  as  the  the  previous  example  shows, 
the  lead  loses  1.4  ounces,  the  weight  of  a  volume  of  water 
equal  to  the  cork  is  9.4 — 1.4  =  8  ounces.  Therefore,  the 
specific  gravity  of  the  cork  is  2  -r-  8  =  .25. 

154.  A  floating  body  has  a  constant  weight,  but  dis- 
places a  greater  volume  of  light  than  of  heavy  liquids.     Hence, 
if  these  relative  volumes  may  be  found,  the  specific  gravity 
of  any  liquid  may  be  found  by  dividing  the  volume  which 
a  floating  body  displaces  in  water,  by  the  volume  which  it 
displaces  in  a  given  liquid.     This  is  the  principle  of  the 
hydrometer. 

The  hydrometer  consists  of  a  glass  stem,  near  the  bottom 
of  which  are  blown  two  small  bulbs.  Some  mercury  or  shot 


THE  HYDROMETER. 


101 


is  placed  in  the  lower  bulb,  to  serve  as  ballast,  and  the 
point  to  which  the  instrument  sinks  in  pure  ~<vat«^r;  fa  marked 
on  the  stem.  It  is  then  placed  in  a  liquid  wh6se  specific 
gravity  is  known;  the  point  to  which"  it  sral^s 
and  the  intermediate  space  sub- 
divided into  equal  spaces,  called 
degrees.  The  value  of  these  de- 
grees in  terms  of  specific  gravity 
is  then  determined  by  a  mathe- 
matical calculation.  These  in- 
struments do  not  give  accurate 
results,  but  are  of  convenience 
for  rapid  determinations. 

A  farmer  roughly  esti- 
mates the  density  of  brine 
by  noticing  whether  an 
egg  or  a  sound  potato 
will  float  in  it. 

The  specific  gravity  of  liquids  is  accurately  found 
by  the  specific  gravity  bottle,  Fig.  81,  by  means  of 
wrhich  wre  are  enabled  to  weigh  equal  volumes  of 
two  liquids. 

The  iveiciht  of  any  qiven  liquid 

mi ^~jTf —     —  i     i ~? — i — =Specific  gravity. 

The  weight  oj  an  equal  volume  of  water 

155.   The  specific  gravity  of  gases  is  found  in  the  same 
way,  only  it  is  necessary  to  use  very  large  flasks. 


FIG.  80. 


RECAPITULATION. 

I.  Liquids  are  both  compressible  and  elastic. 

IT.  They  produce  pressure   by  their  weight,  proportional  to  their 
depth,  and  transmit  it  as  if  it  were  an  external  pressure. 

ITT.  They  transmit  external  pressure  in  every  direction, 


102  ELEMENTS  OF  PHYSICS. 

1.  Undiminished. 

,  -,.         2*.  Perpendicular  to  their  surfaces. 
3.  PrQ|)»)riiGiial  to  their  areas. 

IV.  A  liquid  always  ?eeks  its  lowest  level. 

V.  The  surface  of  a  liquid  at  rest  is  horizontal. 

VI.  The  upward  pressure  of  a  liquid  upon  a  solid  is  equal  to  the 
weight  of  the  fluid  displaced. 

1.  A  submerged  solid  loses  weight  equal  to  the  weight  of  the 

fluid  of  the  same  volume. 

2.  A  floating  solid  loses  all  its  weight,  and  displaces  a  volume 

of  the  fluid  equal  to  this  weight. 

VII.  The   standards  for  specific  gravity  are  water  for  solids  and 
liquids ;  and  air  for  gases.     The  normal  conditions  are  a  temperature 
of  30. °1  F.  for  water  and  32°  F.  for  all  other  bodies,  and  a  barometric 
pressure  of  29.922  inches. 

VIII.  The  specific  gravity  of  a  body  is  found  by  comparison  with 
water  and  air. 

1.  By  the  relative  weights  of  equal  volumes. 

2.  By  the  relative  volumes  of  equal  weights. 

PROBLEMS. 

1.  A   reservoir  is  120  feet   long,  40  feet  wide,  and   20  feet  deep; 
what  is  the  weight  of  the  water  contained  in  it?    What  is  the  pres- 
sure on  the  bottom?    On  each  side?    The  total  pressure? 

2.  A  mass  of  galena  weighs  6  ounces   in   air  and  4.8  ounces   in 
water;  what  is  its  specific  gravity?'^ 

3.  The  same  mass  attached  to  an  ounce  of  cork  weighs  in  water 
2.7  ounces;  what  is  the  specific  gravity  of  the  cork? 

4.  A  flask  contains  900  grains  of  water,  800  grains  of  alcohol,  "or 
1,350  grains  of  sulphuric  acid;   what  is   the  specific  gravity  of  the 
alcohol?    Of  the  acid? 

5.  A  boy's  marble  weighs  in  air  450  grains,  in  water  300  grains,  in 
coal-oil  350  grains;   required,  the  specific  gravity  of  the  marble  and 
of  the  coal-oil. 

C.  If  the  upper  board  of  the  hydrostatic  bellows  has  an  area  of  100 
square  inches,  and  a  boy  standing  upon  it  raises  water  in  the  pipe 
to  the  height  of  30  inches,  what  is  the  weight  of  the  boy?  /  (}  \ 


CHAPTEK  X. 

FLUIDS   IN   MOTION. 

156.    We  learned,  in  the  preceding  chapter,  that  the  press- 
ure of  a  fluid  is  proportional  to  its  depth.       Hence,  if  a 


. 


FIG.  82. 

vessel  be  filled  with  a  liquid,  and  apertures  r,  q,  m,  n,  p, 
be  opened,  the  liquid  will  flow  out  with  unequal  velocities, 
being  less  for  r  than  for  any  point  beneath  it,  and  equal  for 
any  two  points  at  equal  depth  below  the  surface,  as  p  and  v. 
But  the  velocity  does  not  increase  in  the  simple  ratio  of  the 
depth.  The  jet  at  v  tends  to  '  rise  to  the  level  at  h,  and 
falls  short  of  it  only  because  of  friction,  the  resistance  of 
the  air,  and  the  weight  of  the  particles  falling  back.  If, 
then,  the  velocity  at  v  is  sufficient  to  carry  the  liquid 
through  the  vertical  distance,  vh,  in  opposition  to  gravity, 
this  velocity  must  be  equal  to  tJiat  which  a  body  would  acquire  in 
falling  through  the  same  space;  and  this  must  be  true  for  any 

(103) 


104  ELEMENTS  OF  PHYSICS. 

aperture.  Hence  (by  page  60),  the  velocity  with  which 
a  liquid  escapes  from  an  orifice  increases  with  the  square 
root  of  the  depth  below  the  surface. 

157.  The  course  of  a  stream  spouting  out  in  any  other 
direction  than  the  vertical,  is  that  of  a  parabola.     We  can 
easily  calculate  the  range  of  a  horizontal  jet.     For  example : 
if  the  jet,  q,  is  four  feet  below  the  surface,  the  velocity  due 
to  the  depth,  hq,  is  sixteen  feet  per  second.      If  its  height 
above  a6,  the  level  on  which  it  strikes,  is  nine  feet,  it  will 
be   three-fourths  of  a  second  in  falling.     As  these  two   mo- 
tions  do  not   interfere   with   each   other,   the   range  will  be 
found  by  multiplying  the  velocity  by  the  time  (16  X  f  =  12). 
The  range  of  a  jet  will  be  the  greatest  when  it  is  midway  be- 
tween the  surface  and  the  level  at  which  it  strikes.     Any 
orifice,  as  n,  as  far  below  the  middle  point  as  q  is  above  it, 
wrill  have  an  equal  range  with  q,  for  although  its  velocity  is 
greater,  it  has  a  less  time  to  fall,  and.  the  products  are  the 
same  in  both  cases.      (The  resistance  of  the  air  being  re- 
moved.) 

158.  The  flow  of  water  in  pipes  is  much  retarded  by 
friction  and  other  causes,  and,   unless   a  large   allowance  is 
made  for  these,  the  quantity  delivered  will  fall  short  of  the 
estimate.      Under  ordinary   circumstances,   the    diameter    of 
the  discharge  pipe  should  be   one-half  greater  than  that  re- 
quired by  theory. 

159.  Running  water  acts  as  a  motive  power   (1)  by  its 
weight,  (2)  by  the  force  of  the  current,  or  (3)  by  the  com- 
bined  effect   of  both.      Water-wheels   are   either  vertical   or 
horizontal.      In  vertical   wheel,  the   effective   power   of   the 
stream  is  applied  to  buckets  or  boards  fixed  on  the  circum- 
ference.    The  wheel  is  connected  with  the  machinery  to  be 
moved.     There  are  three  varieties  of  vertical  wheels :    (1) 
the  overshot,   (2)   the  undershot,  and   (3)   the  breast-wheel, 


WATER-WHEELS. 


105 


which  receive  their  names  according  as  the  water  strikes 

near  the  top  of  the  wheel,  as 
in  Fig.  83;  or  at  the  bottom, 
as  in  Fig.  84;  or  somewhere 
near  the  axis,  as  in  Fig.  85. 


FIG.  83. 


FIG.  84. 

160.   The   availability   of  any  wheel   depends  on  the 
character  of  the  fall.     Undershot  wheels  are  adapted  to  low 


FIG.  85. 

falls  or  rapids  with  large  supplies  of  water.  Overshot 
wheels  are  used  with  falls  not  exceeding  sixty  feet  in  height, 
and  are  efficient  even  with  small  streams.  Breast-wheels 
require  a  larger  supply  of  water,  but  the  fall  is  always  less 
than  their  diameter. 

161. '  There  are  two  forms  of  horizontal  wheels ;  (1)  the 
reaction,  (2)  the  turbine. 


106 


ELEMENTS  OF  PHYSICS. 


The  reaction  wheel  acts  on  the  principal  of  unbalanced 
lateral  pressure  (page  95). 

A  vertical  axis,  CD,  which  re- 
volves upon  a  pivot,  terminates  in 
in  two  horizontal  pipes,  A  and  J5, 
whose  extremities  are  curved  in  op- 
posite directions.  As  the  fluid  es- 
capes from  the  orifice  in  the  ends  of 
these  pipes,  the  arms  are  driven 
around  in  opposite  directions  to 
the  flow,  and  may  be  employed  to 
communicate  motion  to  machinery. 

162.  There  are  three  classes  of  turbines,  and  many 
varieties  of  each  class.  One  of  the  most  efficient  was  in- 
vented in  1827,  by  M.  Fourneyron.  Fig.  87  shows  a  verti- 
cal, and  Fig.  88,  a  horizontal  section  of  this  turbine. 

A  column  of  water,  con- 
fined in  a  cylinder,  B, 
after  descending  in  its 
vertical  axis,  rushes  out 
at  the  bottom,  through  a 
great  number  of  guides, 
</,  so  as  to  strike  the 


FIG.  86. 


FIG.  87.  FIG.  88. 

curved  buckets,  6,  of  the  wheel,  and  make  it  revolve.  The 
buckets  are  so  curved  as  (1)  to  receive  the  impulse  of 
the  water  in  the  direction  of  its  greatest  efficiency ;  and  then 


TURBINES.  107 

(2)  to  permit  its  escape  with  the  least  loss  of  motion.  The 
wheel  is  connected  beneath  the  cylinder  to  the  shaft,  d, 
which  passes  upward  through  the  center  of  the  cylinder, 
and  communicates  its  motion  to  the  gearing  at  the  upper 
end  of  the  shaft.  Turbines  are  applicable  to  falls  of  any 
height,  from  nine  inches  upward,  and  will  utilize  from  .75 
to  .90  of  the  power  of  the  water. 

RECAPITULATION: 

I.  The  velocity  of  a  liquid  jet  is  that  which  a  body  would  acquire 
in  falling  through  a  space  equal  to  its  depth  helow  the  surface. 

II.  Running  water  exerts  a  power  in  proportion  to  its  weight  and 
the  square  of  its  velocity,   diminished  by  the  impediments  to  mo- 
tion. 

III.  It  acts  as  a  motive  power  in  water-wheels: 

Useful 
Effect. 

("Undershot 25 

1.  Vertical j  Breast  60 

'-Overshot 75 

/Reaction 40 

2.  Horizontal 1 

I  Turbine  80 

PROBLEMS. 

1.  A  reservoir  of  water  is  64   feet  high ;    with  what  velocity  will 
water  flow  from  an  orifice  16  feet  below  the  surface?    25  feet?    32 
feet?    64  feet?    What  are  the  ratios  between  these  velocities?    What 
will  be  the  range  of  a  stream  escaping  from  an  orifice  at  the  center 
of  the  reservoir? 

2.  Suppose  a  pipe  an  inch  in  area  was   attached  to  each  of  these 
orifices,  what  would  be  the  theoretical   discharge  of   water  per  min- 
ute? 

3.  The  source  of  the  Mississippi  is  1,572  feet  above  its  mouth ;   if 
its  flow  were  entirely  unimpeded,  what  would  be  its  final  velocity? 


CHAPTER    XI. 

THE   PHENOMENA    OF   AERIFORM   FLUIDS. 

163.  The  atmosphere  is  mainly  a  mixture  of  two  gases, 
oxygen  and  nitrogen.     These  constituents  have  never  been 
obtained  in  a  solid  or  a  liquid  state.     Most  gases  have  been 
condensed  into  liquids  by  the  aid  of  pressure  and  of  low 
temperature,   and  some  so  easily  that  they  are  frequently 
considered  as  a  separate  class  under  the  name  of  vapors. 
Steam  is  the  type  of  all  vapors.     Nevertheless,  there  is  no 
difference  between  a  vapor  and  a  gas,  except  such  as  results 
from  their  specific  properties,  as  density,  odor,  etc.     Hence, 
whatever  physical   property  may  be   established  regarding 
atmospheric    air,    will    be    understood    as    applying    to    all 
bodies,  so  long  as  they  are  in  the  aeriform  state. 

164.  Air  has  been  proved  to  possess  extension,  impen- 
etrability, compressibility,  mobility,  and  inertia,  wrhich  are 
essential    properties  of  matter.      Like   all    other  fluids,    it 
transmits  pressure  undiminished  in  every  direction;  but,  as 
its  compressibility  far  exceeds  liquids  like  water,  the  effect 
of  pressure  is  not  felt  as  instantaneously  at  long  distances  as 
in  the  case  of  liquids. 

165.  The  air  is  kept  in  its  place  about  the  earth  by  the 
joint  action  of  the  attraction  of  gravitation  and  the  repul- 
sive force  which  exists  between  its  molecules.     Consequently, 
the  atmosphere,  at  its  upper  limit,  must  have  a  definite  sur- 
face like  the  sea.     At  any  point  on  the  earth's  surface,  the 
air  will  exert,  by  reason  of  gravity,  a  pressure  due  to  a  line 
of  molecules  extending  from  that  point  to  the  upper  limit 
of  the  atmosphere. 

(108) 


PRESSURE  OF  THE  ATMOSPHERE. 


109 


166.   The  pressure  of  the  atmosphere   may  be  illus- 
trated by  many  simple  experiments. 


FIG.  91. 


FIG.  89. 

(1)  In  the  pneu- 
matic inkstand,  Fig. 
89,    the    downward 
pressure  of  the  at- 
mosphere   on    the 

liquid  in  the  tube  FlG-  90- 

sustains  the  ink  in  the  bottle.  When  the 
ink  sinks  down  to  the  level  of  the  neck, 
a  bubble  of  air  passes  in  and  forces  out  a 
portion  of  the  ink  into  the  tube. 

(2)  Fill    a    tumbler    with    water,    and, 
having  placed  a  thick  slip  of  paper  over 
its  mouth,  press  the  paper  down   tightly 

with  the  hand,  and  invert  the  glass  cautiously.  The  hand 
may  now  be  removed,  and  the  water  will  be  supported  in 
the  glass  by  the  upivard  pressure  of  the  atmosphere  on  the 
paper,  Fig.  90. 

(3)  Take  a  small  open  tube,  or  a  pipette,  Fig.  91,  plunge 
it  vertically  in  water  until  it  is  filled,  then  close  the  upper 
end  with  the  finger  and  raise  the  tube.     The  water  will  not 
run  out  because  the  pressure  of  the  air  keeps  it  up.     Re- 
move the  finger,  so  that  the  atmosphere  may  press  above 
and  below,  and  the  water  will  fall  by  its  own  weight. 

(4)  Water  will  not  flow  out  of  a  small  tap  in  a  tight 
barrel,  because  of  the  lateral  pressure  of  the  atmosphere.     If 
this  be  counteracted   by  admitting  air  through  an  opening 
in   the  top,   the  water   will  run   freely  by  its  own  weight. 


110  ELEMENTS  OF  PHYSICS. 

No  upper  opening  is  required  in  beer  barrels,  because  of  the 
tension  of  the  gases  contained  in  the  beer. 

(5)  A  boy's  sucker  is  made  by  attaching  a  stout  string  to 
the  center  of  a  small  circular  piece  of  thick  leather.  The 
leather  is  first  soaked  in  water,  and  then  pressed  firmly 
against  the  smooth  surface  of  a  stone,  so  as  to  exclude  all 
the  air.  The  two  surfaces  are  now  held  to-  ,,ttii/^\ 
gether  by  the  force  of  fifteen  pounds  to  the 
square  inch,  Fig.  92.  On  pulling  the  string, 
a  vacuum  is  formed  under  a  portion  of  the 
leather,  and  the  weight  of  the  atmosphere  on 
its  upper  side  is  borne  by  the  hand.  The 
weight  of  the  atmosphere  is  thereby  removed 
from  this  portion  of  the  stone,  and,  if  it  is 
not  too  heavy,  the  pressure  of  the  atmosphere  FIG.  92. 
on  its  under  side  will  raise  it  up. 

167.  The  barometer,  described  on  page  20,  is  used  for 
measuring  atmospheric  pressure.     At  the   level  of  the  sea, 
the  mercurial  column  varies  in  height  from  twenty-eight  to 
thirty-one   inches,   the  average   being,   for  London,   29.922 
inches.     This  pressure  will  sustain  a  column  of  water  33.9 
feet  high. 

168.  Mercury  is  about  eleven  thousand  times  denser 
than  the  air  at  the  level  of  the  sea.     If  the  air  were  every- 
where of  this  density,  the  height  of  the  atmosphere  required 
to  balance  the  barometric  column  would  be  11000  X  -29.922 
inches,  or  twenty-seven  thousand  four  hundred  feet.     The 
pressure  of  the  air  may,  therefore,  be  reckoned  as  equal  to 
a  column  5.2  miles  high,  having  throughout  a  density  equal 
to  that  of  air  at  the  sea  level. 

We  know  that  aeronauts  have  ascended  seven  miles.  We 
know  also  that  the  air  must  become  rarer  as  wre  ascend  from 
the  level  of  the  sea,  because  the  air  at  any  level  is  com- 


PRESSURE  OF  THE  ATMOSPHERE. 


Ill 


pressed  by  the  weight  of  the  column  above  it.  If  a  barom- 
eter were  carried  one  thousand  feet  above  the  sea  level,  the 
column  would  descend  about  an  inch.  At  the  height  of  fifty 
miles,  the  mercurial  column  would  be  elevated  about  one- 
thousandth  of  an  inch.  This  height,  therefore,  may  be  con- 
sidered as  the  practical  limit  of  the  atmosphere. 

INCHES. 

Fig.  93  is  an  attempt  to  represent  to  the  eye 
the  decreasing  pressure  of  the  atmosphere. 

169.  Heights  are  measured  by  the  barom- 
eter, in  accordance  with  the  observed  rate  of  the 
decrease  in  atmospheric  pressure.    Observations 
are  taken  at  two  stations  at  very  nearly  the  same 
moment.       The    difference    between    the    two 
barometric   columns  will   represent   the   differ- 
ence  in   the   atmospheric   columns    above    the 
two  stations,  from  which  the  vertical  distance 
between  the  stations  may  be  calculated. 

170.  The  atmosphere  may  be  regarded  as 

an  aerial  ocean,  in  whose  lower  depths  we  live. 
From  the  extreme  mobility  of  its  particles,  it 
is  never  perfectly  at  rest,  but  moves  in  im- 
mense waves  above  our  heads.  When  the 
crest  of  one  of  these  waves  is  over  the  barome- 
ter, the  column  rises,  and  then  again  falls  as  the  hollow 
of  the  wave  succeeds.  This  will  give  rise  to  variations 
which  are  dependent  on  the  season  and  even  the  hour  of 
the  day,  but  which  succeed  each  other  in  periods  which  are 
very  nearly  regular. 

171.  The  barometer  is  subject  also  to  irregular  varia- 
tions, which  are  often  coincident  with   the   changes  in   the 
weather.     The  absolute  height  of  the  column  varies  with 
the  altitude  of  the  station,  and  affords,  by  itself,  no  indica- 
tion of  the  weather;  hence,  the  weather  marks,  "fair,  rain, 


FIG.  93. 


112 


ELEMENTS  OF  PHYSICS. 


wind,"  on  some  barometers,  are  worthless.  The  barometer 
measures  only  the  pressure  of  the  atmosphere,  and  vari- 
ations in  its  height  indicate  variations  in  this  pressure, 
which,  if  they  occur  at  irregular  intervals,  may  be  followed 
by  changes  in  the  weather. 

.  Rules  for  predicting  changes  in  the  weather  : 

(1)  The  rising  of  the  mercury  indicates  the  approach  of 
fair  weather  ;  the  falling  of  the  mercury  indicates  the   ap- 
proach of  foul  weather. 

(2)  A  sudden  and  great  fall  indicates  a  violent  storm. 

(3)  When    the    barometer  changes    slowly, 
a  long   continuance  of  the  weather  indicated 
may  be  expected. 

(4)  A  sudden  change  of  the  barometer  indi- 
cates that  the  change  of  weather  will  not  be 
of  long  duration.  ^~\*  — 

172.  Thus  far  we  have  considered  the 
air  in  the  free  state  ;  let  us  see  how  it  acts 
when  confined.  Bend  the  closed  end  of  a 
barometer  tube,  as  in  Fig.  94,  and  pour  in 
just  enough  mercury  to  fill  the  bend.  The 
inclosed  air  is  in  its  natural  state,  under  the 
pressure  of  one  atmosphere.  If  thirty  inches 
of  mercury  be  poured  in  the  open  arm,  the 
confined  air  will  be  under  the  pressure  of  two 
atmospheres,  one  of  mercury  and  the  other  of 
air,  and  will  be  reduced  in  volume  one-half. 
If  thirty  inches  more  mercury  be  added,  the 
pressure  will  be  three  atmospheres,  and  the 
volume  will  be  reduced  to  one-third,  and  so  on. 
Therefore:  (li  The  volume  of  a  given  weight  of  air  decreases  as 
the  pressure  to  wJiidi  it  is  exposed  i 


FlG- 


MARIOTTE'S  LAW. 


113 


This  statement  is  known  as  Mariotte's  law,  and  is  true  for 
all  gases  within  small  limits  of  error.  Now,  as  the  volume 
decreases  its  density  increases ;  therefore, 

(2)  The  density  of  a  given  weight  of  air  is  directly  as  tiie  press- 
ure to  which  it  is  subjected. 

Finally,  as  the  pressure  is  always  sustained  by  the  elastic 
force,  or  tension,  of  the  inclosed  air, 

(3)  The  tension  of  a  given  weight  of  air  is  directly  as  the 
pressure  to  which  it  is  subjected. 

Consequently, 

(4)  The  density  and  tension  of  a  given  iveight  of  air  will 
increase  as  its  volume  is  decreased,  and  ivill  decrease  as  its  volume 
increases. 

173.  Mariotte's  law  applies  both  to  con- 
densed and  to  rarified  air.  The  proof  for 
pressures  less  than  one  atmosphere  may  be 
made  by  filling  a  barometer  tube  to  within  four 
inches  of  the  top  with  mercury,  and  then  in- 
verting it  in  a  tall  cistern  of  mercury,  Fig. 
95.  When  the  tube  is  sunk  until  the  level 
of  the  mercury  is  the  same  as  in  the  cistern, 
the  confined  air  will  be  under  the  pressure  of 
one  atmosphere.  When  the  tube  is  raised,  the 
pressure  exerted  on  the  air  will  be  one  atmos- 
phere minus  the  weight  of  the  mercury  raised 
in  the  tube.  If  the  column  is  raised  fifteen 
inches,  the  air  will  have  doubled  its  volume, 
and  will  have  decreased  one-half  both  in 
density  and  in  tension. 


FIG.  95. 


174.    The  tension  of  aeriform  fluids   is  measured   by 
manometers  or  gauges.       One  of  the   simplest    forms  is  the 

PHYS.  10. 


114 


ELEMENTS  OF  PHYSICS. 


FIG.  96. 


closed  manometer,  Fig.  96.     It  consists  of  a  U  tube,  closed 

at  one  end,  and  half  filled  with  mercury.     The  closed  end 

contains   dry  air.     When    the    open    end 

communicates  freely  with  the  atmosphere, 

the  level  of  the  mercury  is  the  same  in 

both  parts  of  the  tube,  showing  that  the 

inclosed  air  is  under  a  tension  due  to  one 

atmosphere. 

Now,  if  the  open  end  is  connected  with 
vessels  containing  aeriform  fluids  whose 
tension  is  to  be  measured,  as  with  steam 
in  a  boiler,  the  confined  air  will  be  reduced  in  volume  to 
one-half,  one-third,  etc.,  according  as  the  pressure  increases 
to  two,  three,  etc.,  atmospheres.  Or,  if  the  pressure  is  less 
than  one  atmosphere,  the  inclosed  air  will  expand  as  the 
pressure  decreases. 

AfR-PUMPS. 

175.  \An  air-pump  is  an  instrument  for  removing  the  air 
from  a  closed  vessel^ 

Fig.  97  shows  the  Leslie  air-pump,  and  Fig.  98  the  same 
instrument  in  section.  The  receiver,  It,  is  connected  with 
the  cylinder,  C,  by  a  long  bent  tube,  terminating  in  a  hori- 
zontal brass  plate.  The  mouth  of  the  receiver  and  the  sur- 
face of  the  brass  plate  are  carefully  ground,  so  as  to  bring 
them  in  contact  at  every  point.  The  edge  of  the  receiver 
is  smeared  with  grease,  so  as  to  render  the  connection  as 
close  as  possible. 

When  the  piston,  P,  is  raised  from  the  bottom  of  the 
cylinder,  the  external  air  closes  the  upper  valve ;  the  air  in 
the  receiver  expands,  opens  the  lower  valve,  and  fills  the 
cylinder.  When  the  piston  is  depressed,  the  lower  valve 
closes,  and  the  air  in  the  cylinder  is  forced  through  the 


THE  AIR-PUMP. 


115 


upper  valve  out  into  the  atmosphere.     As  the  piston  again 
rises    the   upper   valve  is   closed,   the    lower  valve    opens, 


FIG.  97. 

and  the  confined  air  expands  into  the  cylinder.  At  every 
ascent  and  descent  of  the  piston, 
a  portion  of  air  is  removed  from 
the  receiver;  and  this  process  may 
be  repeated  until  the  tension  of 
the  air  remaining  is  not  sufficient 
to  lift  the  lower  valve.  The  re- 
ceiver is  then  said  to  be  exhausted. 
The  tension  of  the  air  in  the 
receiver  is  measured  by  a  gauge, 
which  consists  of  a  bent  tube, 
leading  from  the  receiver  to  a  ves- 
sel of  mercury,  H.  The  external  air  forces  the  mercury  up 
the  gauge,  in  proportion  as  the  tension  of  the  air  in  the 


116  ELEMENTS  OF  PHYSICS. 

tube  is  diminished.  If  the  exhaustion  were  perfect,  the 
mercury  would  rise  to  about  thirty  inches.  The  height  of 
the  gauge  indicates  the  difference  between  the  pressure  of 
the  atmosphere  and  the  tension  of  the  air  in  the  receiver. 

The  air-pump  is  also  provided  with  a  stop-cock,  S,  to 
close  the  communication  between  the  cylinder  and  receiver 
when  required.  The  stopper,  A,  is  used  to  admit  the  ex- 
ternal air  to  the  receiver.  A  third  valve,  t,  is  usually 
placed  in  the  top  of  the  cylinder  to  prevent  the  external 
air  from  pressing  on  the  piston. 

176.  The  air-pump  may  be  used  to  perform  a  great  va- 
riety of  experiments,  illustrating  the  properties  of  the  air, 
only  a  few  of  which  can  here  be  given. 

(1)  The  presence  of  air  in  bodies  may  be  shown  by  placing 
a  jar  of  well-water  under   the  receiver.     On   working  the 
pump,   bubbles  of  air  will  be  disengaged  from   the  Avater. 
Having  freed  the  water  from   air,  fasten   to  the  bottom  of 
the  jar  bits  of  wood  or  other  solids,  and  repeat  the  experi- 
ment.    The  formation  of  air  bubbles  will  prove  their  poros- 
ity, and  the  presence  of  air  in  the  pores. 

(2)  Expansibility.     Tie  the  neck  of  a  fresh,  flaccid  bladder 
and   place  it  in  the  receiver.     On  exhausting  the  receiver, 
the  bladder  will  dilate,  because  the  air 

within  it  expands.  On  re-admitting 
air  to  the  receiver,  the  air  in  the 
bladder  resumes  its  former  volume. 

A  withered  apple,  or  a  bunch  of 
shriveled  grapes  will  become  plump  in 
an  exhausted  receiver. 

(3)  Pressure  of  the  atmosphere.    Take 
a  small  open  receiver,  close  the  upper 

end  tightly  with  a  piece  of  moistened  bladder,  and  suffer  the 


THE  MAGDEBURG  HEMISPHERES. 


117 


bladder  to  dry.  On  exhaustion,  the  external  pressure  will 
generally  be  sufficient  to  burst  the  bladder  with  a  loud 
report.  If  the  bladder  is  very  stout,  or  the  exhaustion  in- 
complete, it  may  be  necessary  to  weaken  the  strength  of 
the  membrane  by  puncturing  it  with  the  point  of  a  pin. 

(  The  Magdeburg  Jiemispheres,  Fig.  100,  consist  of  two  hollow 

brass  hemispheres,  which  fit  together  air- 
tight, j   One   of  them   may   be   connected 

with  the  air-pump  by  a  tube  and  stop-cock 

arrangement.  /On  exhausting  the  air  from 

the  interior,  the  two  hemispheres  will  be 

held  together  with  a  force  of  fifteen  pounds 

to  the  square  inch.\   If  their  diameter  is 

three  inches,  the  area  of  the  section  will 

be  seven  inches,  and  the  force  which  holds 

them  together  will  be  over  one  hundred 

pounds.  \^s  the  restraining  force   is  the 

same  in   every  position  in  which  they  are  FIG.IOO. 

held,   the  pressure  of  the  atmos- 
phere is  Hie  same  in  every  direction^ 

Fig.  101  represents  a  tall  re- 
ceiver, which  terminates  in  a 
metallic  cap,  furnished  with  a 
stop-cock,  a  screw,  and  an  in- 
terior jet  pipe.  Exhaust  the 
air  from  the  interior  and  close 
the  stop-cock.  Place  the  mouth 
of  the  tube  under  water  and 
open  the  stop-cock.  The  press- 
ure of  the  atmosphere  will  drive 
the  water  up  the  pipe,  form- 
ing what  is  known  as  the 
vacuum  fountain. 


FIG.  101. 


118 


ELEMENTS  OF  PHYSICS. 


FIG.  102. 


The  weight  lifter  consists  of  a  receiver,  which  is  connected 
to  the  air-pump  by  an  opening  in  the  top.  The  lower  end 
is  closed  by  a  piston  or  by  a  stout  rubber  bag.  When  the 
air  is  withdrawn  from  the  receiver,  the  bag 
is  forced  upward,  and  carries  with  it  weights 
attached  below.  If  the  receiver  is  five 
inches  in  diameter,  nearly  three  hundred 
pounds  will  be  lifted  by  the  upward  pressure 
of  the  atmosphere,  if  the  vacuum  is  complete. 

(4)  When  a  heavy  weight  is  thus  sus- 
tained, the  elasticity  of  the  air  may  be  shown, 
in  a  striking  manner,  by  forcing  down  the  load  by  the  hand, 
and  then  releasing  it.  The  weight  will  then  oscillate  up 
and  down,  as  if  on  an  elastic  spring. 

(5)\JZVie  weight  of  air  may  be  ascertained,  by  taking  a 
vessel  of  known  capacity  and  finding  the  difference  of  its 
weight  when  filled  with  dry  air,  and  when  exhausted  of  air. 
If  the  capacity  of  the  vessel  is  one  hundred  cubic  inches, 
the  difference  of  its  weight  will  be  thirty-one  grains.  There- 
fore, the  weight  of  one  cubic  inch  of  air  is  0.31  grains,  j) 

(6)  The  buoyancy  of  air. 
By  the  principle  of  Archim- 
edes, a  solid  immersed  in 
a  fluid  loses  an  amount  of 
weight  equal  to  the  weight 
of  an  equal  volume  of  the 
fluid.  Hence,  every  sub- 
stance weighs  less  in  air  than 
in  vacuo. 

Suspend  to  one  arm  of  a 
balance  a  hollow  globe,  or  a 
FIG.  103.  ball  of  cork,  and  counter- 

poise it  with  a  lead  weight.  Now  place  the  balance  under 


THE  BALLOON.  119 

a  receiver  and  exhaust  the  air.  The  globe  or  the  cork 
will  fall,  and  thus  seem  to  be  heavier  than  the  lead. 

If  a  body  is  lighter  than  an  equal  volume  of  air,  it  will 
rise  in  it.  Smoke  rises  in  a  chimney  because  air  is  rarified 
by  heat.  A  soap-bubble,  filled  with  warm  air,  rises  because 
it  weighs  less  than  the  air  it  displaces.  If  the  soap-bubble 
is  filled  with  hydrogen,  it  rises  rapidly  until  it  bursts. 

v  Balloons  are  varnished  silk  bags,  filled  with  hydrogenj 
The  buoyant  effort  of  the  air  in  raising  a  balloon  is  equal  to 
the  difference  between  the  weight  of  the  gas  used  and  the 
air  displaced  by  it.  A  spherical  balloon,  forty  feet  in  diam- 
eter, will  displace  two  thousand  five  hundred  pounds  of  air, 
but  will  contain  less  than  two  hundred  pounds  of  hydrogen. 
The  lifting  force  of  such  a  quantity  of  gas  is  over  a  ton. 
It  is,  therefore,  capable  of  lifting  the  weight  of  the  balloon, 
the  aeronaut,  and  a  large  quantity  of  sand  used  for  ballast. 
If  the  aeronaut  wishes  to  descend  from  a  height,  he  allows 
some  of  the  gas  to  escape,  by  opening  a  valve  in  the  balloon. 
If  he  wishes  to  rise  again,  he  throws  out  a  portion  of  his 
ballast^— 

(7)  \That  air  is  necessary  to  combustion,  may  be  shown  by 
placing  a  lighted  candle  in  a  receiver.  On  working  the 
pump,  the  candle  will  grow  dimmer,  burn  blue,  and  finally 
go  out.  The  smoke  of  the  candle  will  be  seen  to  descend 
because  there  is  nothing  to  sustain  it. 

(8) /That  air  is  necessary  to  animal  life,  may  be  shown  by 
placing  a  bird  or  a  mouse  in  a  receiver.  On  exhausting  the 
air,  the  animal  will  give  evident  signs  of  distress,  and  will 
soon  die. 

(9)  The  relations  of  air  to  sound  and  heat  will  be  consid- 
ered hereafter. 


U77. 


The  body  of  a  man  of  average  size  has  a  surface 


120  ELEMENTS  OF  PHYSICS. 

of  about  two  thousand  square  inches.  He,  therefore,  sus- 
tains, at  the  level  of  the  sea,  a  pressure  of  thirty  thousand 
pounds.  It  conveys  a  wrong  notion  to  speak  of  this  press- 
ure as  a  load ;  on  the  contrary,  the  buoyant  effort  of  the 
air  lifts  the  man,  and  makes  him  press  the  ground  more 
lightly  than  he  would  without  it.  The  atmosphere  acts  on 
all  sides  of  a  body  immersed  in  it,  not  as  a  weight,  but  as 
a  crushing  force.  The  reason  why  we  do  not  feel  this  com- 
pressing force  is  because  the  pressure  is  transmitted 
throughout  the  body  by  the  blood  and  other  fluids  of  the 
body.  Hence,  when  the  atmosphere  tends  to  squeeze  in 
the  sides  of  the  blood-vessels,  it  is  met  by  an  equal  out- 
ward pressure,  caused  by  the  pressure  of  the  atmosphere  on 
the  other  parts  of  the  system. 

MVe  may  become  sensible  of  this  outward  pressure  by 
placing  the  hand  on  a  small  open  receiver  and  exhausting 
the  air  from  beneath  it.  The  external  air  now  acts  as  a 
load,  holding  the  hand  firmly  to  the  receiver.  The  blood, 
in  the  under  surface  of  the  hand,  distends  the  vessels, 
and,  if  the  skin  has  been  punctured  with  a  pin,  the  blood  is 
forced  out.  Cupping-glasses  are  made  to  act  on  the  same 
principle,  tf 

\  178.  The  condenser  is  an  instrument  for  forcing  a  large 
amount  of  air  into  a  closed  vessel.  \ 

One  of  the  best  forms  is  shown  in  Fig.  104.  It  consists 
of  a  cylinder,  0,  in  which  a  solid  piston  works  air-tight. 
There  are  two  valves  in  the  cylinder,  (1)  the  lateral  valve, 
a,  which  opens  from  the  outside,  and  (2)  the  lower  valve,  b, 
which  opens  from  the  inside.  The  receiver,  R,  may  be  con- 
nected by  a  screw  to  the  cylinder,  and  may  be  opened  or 
closed  by  means  of  stop-cocks  arranged  as  in  the  figure. 

In  using  this  instrument,  the  condenser  and  receiver  are 
connected  and  the  piston  driven  down.  This  action  con- 


THE  AIR-GUN. 


121 


denses  the  air  in  the  cylinder  enough  to  close  the  lateral 
valve  and  open  the  lower.  When  the  piston  has  reached 
its  lowest  point,  all  the  air 
will  be  forced  out  of  the 
cylinder  into  the  receiver. 
The  confined  air  will  have 
its  volume  diminished  and 
its  tension  increased.  If 
the  cylinder  and  receiver 
are  of  the  same  size,  the 
condensed  air  will  have  a 
tension  of  two  atmospheres. 
On  raising  the  piston,  the 
tension  of  the  air  in  the  re- 
ceiver will  close  the  lower 
valve,  the  external  atmos- 
phere will  open  the  lateral 
valve,  and  again  fill  the 
cylinder. 

This  operation  may  be  re- 
peated until  the  receiver  is 
filled  with  air  of  the  tension 
desired.  When  the  receiver  Fro.  104. 

is  thus  charged,  the  stop-cock,  T7,  is  closed,  and  the  cylinder 
is  detached. 

By  bringing  the  lateral  valve  in  communication  with  a 
reservoir  containing  any  gas  whatever,  this  gas  will  be  with- 
drawn from  the  reservoir  and  forced  into  the  receiver.  In 
this  manner  liquids  placed  in  the  receiver  may  be  charged 
with  gases. 

179.  An  air-gun  consists  of  a  charged  receiver,  properly 
connected  to  a  gun -barrel.  After  fitting  a  bullet  to  the 

bottom  of  the  barrel,  a  trigger  turns  the  stop-cock,  and  the 
PHYS.  11. 


122 


ELEMENTS  OF  PHYSICS. 


condensed  air  rushes  out  with  great  force.     A  boy's  pop-gun 
also  illustrates  the  tension  of  confined  air. 

A  fountain  can  be  arranged  to  play 
by  condensed  air.  Before  charging 
the  receiver  fill  it  partially  with  wa- 
ter, and  connect  to  the  stop-cock  a 
tube  reaching  to  the  bottom  of  the 
receiver.  When  the  air  has  been  con- 
densed and  the  stop-cock  is  opened, 
the  air  will  force  the  water  in  a  jet 
to  a  height  proportional  to  the  tension. 

The  experiment  may  be  varied  by  FIG.  105. 

making  the  stream  turn  a  horizontal  tube,  arranged  on  the 
principle  of  the  reaction  wheel,  Fig.  105. 

180.  If  we  place  one  end  of  an  open  tube  in  water, 
and  apply  the  mouth  to  the  other  end,  we  may  cause  the 
liquid  to  rise  in  the  tube  by  suction.  Correctly  speaking, 
the  effect  of  the  suction  is  to  diminish  the  pressure  in  the 
tube;  the  water  is  then  forced  up  the  tube  by  the  pressure 
of  the  atmosphere  on  the  surface  of  the  water  in  the  vessel. 
The  common  suction,  or  lifting-pump,  acts  on  the  same 
principle.  It  consists  of  a  barrel,  B,  similar  to  the  cylinder 
of  the  air-pump,  and,  like  it,  fitted  with  a  piston,  P,  work- 
ing air-tight,  and  two  valves,  U  and  e,  both  opening  upward. 
From  the  bottom  of  the  barrel  proceeds  the  suction-pipe,  0, 
which  dips  below  the  surface  of  the  water  to  be  raised. 

When  the  piston  is  worked,  the  air  beneath  it  is  rarefied 
more  and  more  at  each  stroke ;  the  pressure  of  the  atmos- 
phere causes  the  water  to  rise  in  the  pipe  and  enter  the  cyl- 
inder through  the  lower  valve.  Now,  on  forcing  down  the 
piston,  the  lower  valve,  e,  is  closed,  the  water  forces  open 
the  piston -valve,  C7,  and  rises  above  it.  When  the  piston 
is  again  raised,  the  upper  valve,  U,  is  closed,  and  the  water 


THE  SUCTION -PUMP. 


123 


above  it  is  lifted  to  the  spout  of  the  pump.  At  the  same  time, 
the  atmospheric  pressure  on  the  water  in  the  reservoir,  causes 
more  water  to  rise  into  the  bar- 
rel under  the  piston.  I — . 

181.  The  length  of  the  suc- 
tion-pipe    can     never    exceed    /   { 
thirty -four     feet,    because     the 
pressure-  of   the    atmosphere    is       \> 
capable  of  supporting  a  column  _^ 
of    water    only    thirty-four   feet 
high.     Owing    to    variations   in 
atmospheric    pressure,    and    the 
imperfect     mechanism    of    the 
pump,  the   limit,  in  practice,  is 
less  than  twenty-eight  feet.  There 

is,  however,  no  limit  to  the  height  j 
through  which  water  may  be 
lifted  after  it  has  once  passed 
above  the  piston.  In  deep  wells, 
the  working -barrel,  containing 
the  piston  and  both  valves,  is 
placed  near  the  bottom.  A  long, 
vertical  discharge  -  pipe,  through 
which  the  piston-rod  plays,  con- 
nects the  working -barrel  to  the 
surface  of  the  ground.  The  at-  Flo  106 

mospheric  pressure  forces  the  water  from  the  well  into  the 
working -barrel ;  the  force  applied  to  the  piston  lifts  the 
water  from  the  working-barrel  to  the  top  of  the  discharge- 
pipe. 

182.  In  the  forcing-pump,  the  piston  is  made  solid,  and 
the  upper  valve,  u,  is  placed  in  a  lateral  discharge-pipe,  d, 
connected  with  the  bottom  of  the  barrel. 


124 


ELEMENTS  OF  PHYSICS. 


FIG.  107. 


The  lower  valve  and  suction-pipe  are  the  same  as  in  the 
lifting-pump.  When  the  piston  is  raised,  the  water  passes 
up  the  suction-pipe  through  the  lower  valve,  e,  into  the 
pump -barrel.  On  depressing  the  piston, 
the  lower  valve  closes,  and  the  water  is 
forced  through  the  upper  valve,  u,  into  the 
discharge-pipe.  On  again  raising  the  pis- 
ton, the  upper  valve  closes,  and  prevents 
the  water  in  the  discharge-pipe  from  re- 
turning ;  the  lower  valve  opens  to  admit 
more  water  into  the  barrel.  At  each  de- 
pression of  the  piston,  more  water  is  driven 
into  the  discharge-pipe,  until  it  is  elevated 
to  the  required  height. 

183.  The  water  will  be  ejected  from  such  a  pump  in 
successive  impulses.  When  it  is  desired  to  make  the  stream 
continuous,  an  air-chamber  is  attached,  as  in  Fig.  108.  When 
the  piston  descends,  it  forces  the  water  through  the  valve,  i«, 
into  the  air-chamber,  A ;  the  water  partially  fills  the  chamber, 
and  thus  compresses  the  air.  The  tension 
of  the  compressed  air  increases  as  its  bulk 
is  diminished,  and  soon  becomes  sufficient 
to  force  the  water  in  the  chamber  out 
through  the  tube,  T,  in  a  constant  stream. 

184.  An  ordinary  fire-engine  consists 
of  two  force-pumps,  worked  by  long 
handles,  called  brakes,  and  having  an  air- 
chamber  common  to  both.  The  piston 
of  one  barrel  descends  as  the  other  as- 
cends, by  which  means  a  continuous 
stream  of  water  is  forced  into  the  air- 
chamber,  and  escapes  through  the  dischar'ging-pipe. 
\  185.  The  siphon  is  employed  for  transferring  liquids 


FIG.  108. 


THE  SIPHON  FOUNTAIN. 


125 


from  a  higher  to  a  lower  levelj  It  consists  of  a  bent  tube 
with  two  unequal  arms,  Fig.  109.  In  using  the  siphon,  the 
shorter  arm  is  plunged  in  the  liquid  to  be  transferred.  To 
begin  the  action,  the  air  may  be  removed  from  D  M 
the  tube  by  suction  at  the  lower  end.  The  liquid 
will  be  forced  up  the  shorter  arm  by  the  pressure 
of  the  atmosphere ;  it  will  then  fill  the  tube  and 
continue  to  flow  through  the  siphon. "5 

After  the  suction  is  stopped,  tne  liquid  is 
pressed  up  in  the  shorter  arm  by  the  weight 
of  the  atmosphere  on  the  surface,  A  B,  minus  the  weight  of 
the  liquid  column,  MI.  So,  also,  the  liquid  in  the  longer 
arm  is  pressed  upward  by  the  weight  of  the  atmosphere, 
minus  the  weight  of  the  liquid  column,  M K.  Hence,  the 

liquid  is  urged  in  the  direction, 
CMF,  by  a  force  equal  to  the 
excess  of  the  weight  of  M  K 
over  that  of  ML  If  M  K  and 
M I  were  equal,  there  could  be 
no  flow  in  either  direction.  The 
greater  the  difference  in  the 
length  of  the  arms,  the  greater 
will  be  the  velocity  of  the  flow. 
186.  These  facts  may  be  pret- 
tily shown  by  the  siphon  foun- 
tain. Close  the  mouth  of  a  tall 
flask,  J?,  with  a  cork,  and  insert 
two  glass  tubes,  as  shown  in  Fig. 
110.  The  shorter  arm  should  be 
drawn  out  at  the  upper  end  to  a 
very  fine  bore.  On  exhausting 
the  air  from  the  tube,  the  ordi- 
nary flow  of  the  siphon  will  commence.  If,  now,  the  longer 


FIG.  110. 


126  ELEMENTS  OF  PHYSICS. 

arm  be  lengthened,  by  attaching  a  rubber  tube,  the  jet  may 
be  made  to  strike  forcibly  against  the  top  of  the  flask.  The 
force  of  the  jet  may  be  shown  to  be  dependent  on  the  differ- 
ence in  the  length  of  the  two  arms. 

FRICTION  OF  FLUIDS  AGAINST  EACH  OTHER. 

187.  The  atomizing  tube  is  a  contrivance  for  breaking 
up  the  particles  of  a  liquid 
into  spray.  A  common  form 
is  shown  in  Fig.  111.  It 
consists  of  two  open  tubes, 
so  inclined  to  each  other 
that  a  jet  of  fluid  driven 
through  one  shall  issue  over 
or  near  the  mouth  of  the  FIG.  in. 

other.  The  blast  tube,  A,  is  usually  contracted  at  its  mouth, 
so  as  to  increase  the  velocity  of  the  stream.  The  lower  end 
of  the  suction  tube,  J5,  is  plunged  in  any  liquid,  as  cologne. 

If  a  stream  of  air  is  driven  forcibly  through  the  blast  tube, 
it  will,  on  issuing  from  the  mouth,  drag  the  contiguous  par- 
ticles of  air  along  with  it,  and  thus  produce  a  rarefaction 
behind  it.  As  the  air  is  rarefied  in  the  suction  tube,  B,  the 
atmospheric  pressure  on  the  liquid  will  force  a  column  up- 
ward in  the  tube,  and,  if  the  tube  be  not  too  long,  the  par- 
ticles will  rise  to  the  top.  At  this  point,  the  jet  of  air  will 
drag  the  liquid  molecules  along  with  it,  and  the  two  streams 
will  be  mingled  in  one  of  excessively  fine  spray. 

The  same  principle  is  sometimes  employed  in  producing  a 
draft  in  chimneys  and  locomotives.  In  locomotives  the  waste 
steam  is  driven  through  a  blast  pipe  in  the  smoke  stack,  and 
carries  the  smoke  along  with  it,  and  thus  increases  the  draft 
of  the  fire. 


THE  PNEUMATIC  PARADOX.  127 

188.  The  pneumatic  paradox  affords  another  illustration 
of  the  same  sort.  It  may  be  made  by  taking  two  small 
disks  of  card  board,  and  fitting  to  one  a  small  tube.  Now, 
if  the  other  disk  is  placed  above  the 
tube,  and  a  pin  passed  through  the 
center  to  keep  it  from  sliding,  it  can 
not  be  blown  off  by  any  ordinary  cur- 
rent of  air  driven  through  the  tube. 
Because,  as  the  air  is  driven  between  FIG.  112. 

the  disks,  a  rarefaction  will  be  produced  at  the  center  of  the 
iipper  disk ;  the  air  above  it  will  crowd  it  toward  the  orifice 
and  hold  it  the  more  firmly  as  the  blast  is  made  stronger. 
While  the  current  of  air  is  passing,  the  tube  may  be  held 
in  any  position.  The  force  requisite  to  blow  away  the  upper 
disk  must  exceed  the  atmospheric  pressure  holding  it  down. 

KECAPITULATION. 

1.  Aeriform  fluids  are  governed  by  the  same  laws  as  liquids,  except 
that,  by  reason  of   their  compressibility,  their  volume  is  inversely, 
their  density  and  tension  directly,  as  the  pressure  to  which  they  are 
subjected. 

2.  All  gases,  like  air,  may  be  shown  to  possess  the  universal  proper- 
ties of  matter ;   but,  except  air,  none  are  necessary  to  the  support  of 
animal  life,  and  few  are  concerned  in  ordinary  combustion. 

3.  The  barometer  measures  the  pressure  of  the  atmosphere,  and  may 
be  used : 

(1.)  To  calculate  the  altitude  of  a  place. 
(2.)  To  predict  changes  in  the  weather. 

4.  The  pressure  of    the  atmosphere    is    employed  in   pumps    and 
siphons. 

5.  The  friction  of  fluids  against  each  other  is  employed  in  blast- 
pipes. 


CHAPTER  XII. 

THE  MODES  OF  MOLECULAR  MOTION. 

189.  The  topics  considered  in  the  last  eight  chapters  natu- 
rally fall  into  two  groups.     (1)  Phenomena  which  relate  to 
bodies  in  equilibrium ;    these  belong  to  the  science  of  statics. 
(2)  Phenomena  which  relate  to  bodies  in  motion ;    these  be- 
long to  the  science  of  dynamics.     Statics  and  dynamics  taken 
together  constitute  the  science  of  MECHANICS,  which  treats  of 
bodies  in  equilibrium  and  in  motion. 

Now,  it  will  be  noticed  that  in  these  chapters  we  have 
studied  the  effect  which  force  produces  upon  a  body  taken 
as  a  whole.  It  is  true  that  the  force  of  gravity  acts  upon 
every  molecule  of  a  body,  but  we  have  always  assumed  that 
the  motion  or  rest  of  the  body  did  not  alter  the  relative 
position  of  these  molecules.  Thus,  in  falling  bodies,  and  in 
the  pendulum,  we  considered  only  the  motion  that  was  com- 
mon to  the  entire  mass.  The  molecules  which  made  up  the 
moving  body  did  not  change  their  relative  positions,  and 
were,  therefore,  at  rest  with  respect  to  each  other. 

190.  The  following  chapters  relate  to  motion  among  the 
molecules  of  a  body,  but  which  involve  the  entire  mass  of 
the  body.     These  molecular  movements  sometimes  cause  a 
visible  change   in   the  position  of  the  body,  but  more  fre- 
quently do  not  produce  any  motion  in  the  body  taken  as  a 
whole  that  we  are  able  to  detect  by  our  senses.     We  know 
that  these  molecular  motions  exist   by    the    results   of  the 
motion,  just  as  we  know  that  the  hour-hand  of  a  clock,  or  a 
rifle  bullet,  has  moved  by  the  result  of  the  gross  motion ; 
for  our  senses  do  not  enable  us  to  detect  very  slow  nor  very 

(128) 


UNDULATIONS  OF  SOLIDS.  129 

swift  motions.  When  a  body  expands  by  heat,  we  are  con- 
vinced that  the  result  is  due  somehow  to  a  motiort  among  the 
molecules  of  the  body.  It  would  be  difficult  to  keep  any 
body  at  the  same  temperature  all  the  time ;  and  if  the  tem- 
perature varies,  the  rate  of  molecular  motion  is  increased  or 
diminished,  and  the  body  is  growing  larger  or  smaller.  It 
would  be  still  more  difficult  to  find  a  body  that  did  not  have 
some  motion  among  its  molecules  due  to  the  energy  of  heat, 
that  is,  that  was  in  a  state  of  absolute  cold.  Hence,  on  this 
consideration  alone,  it  is  probable  that  the  molecules  of  even 
the  most  rigid  bodies  are  constantly  in  motion  even  while 
the  body,  as  a  whole,  appears  to  be  in  a  state  of  rest. 

191.  A  pendulum  vibrates  as  a  whole.  The  times  of  its 
vibrations  are  said  to  be  isochronous  ;  that  is,  they  -g 
are  performed  in  equal  times.  If  an  elastic  body  / 
is  bent,  its  molecules  must  have  changed  their  rela-  j 
tive  positions,  because  the  shape  of  the  body  is  al-  E\-  -  D 
tered.  If,  now,  it  is  let  go,  the  molecules  will  tend  \ 
to  assume  their  original  positions,  and,  by  reason  of  \ 
their  elastic  force,  a  series  of  vibrations  will  follow,  AQ> 
which  are  also  isochronous.  To  show  this,  suspend  FlG- 113- 
a  rubber  tube  from  a  hook,  and  stretch  it  taut  by  the  hand. 
Now,  if  the  cord  be  plucked  at  the  center,  it  will  vibrate  in 
the  dotted  lines  shown  in  the  figure,  and  pass  from  D  to  E 
in  precisely  equal  times,  until  it  finally  comes  to  rest.  Such 
vibrations  are  called  transverse  vibrations.  The  greater  the 
disturbing  force,  the  greater  will  be  the  distance  ED.  This 
distance  is  called  the  amplitude  of  the  vibration.  The  greater 
the  amplitude,  the  greater  will  be  the  energy  of  the  vibra- 
tion, but  the  time  required  for  a  vibration  is  unchanged. 

If,  now,  the  cord  be  stretched  by  a  weight,  A,  and  the 
weight  be  pulled  down  and  then  suddenly  let  go,  the  cord 
will  perform  a  series  of  longitudinal  vibrations,  which  are  also 


130  ELEMENTS  OF  PHYSICS. 

isochronous.  That  is,  the  weight,  A,  will  oscillate  alter- 
nately above  and  below  its  normal  position,  while  the  cord 
becomes  alternately  shorter  and  longer.  So,  if  we  twist  the 
weight  around,  it  will  turn  backward  and  forward  in  a 
series  of  isochronous  torsional  vibrations. 

192.  All  elastic  bodies  may  be  thrown  into  alternating 
motions  of  some  sort,  which  are  due  to  the  nature  of  the 
disturbing  force  and  the  elasticity  of  the  body.     If  we  con- 
sider   the   motion  of  only  one  particle,  as  A  or  E,  these 
motions  are  called  vibrations  or  oscillations.     If  we  consider 
the  motions  of  a  line  of  particles,  they  are  called  waves  or 
undulations. 

193.  How  undulations  are  formed  may  be  shown  by 
stretching  a  heavy  rubber  cord  from 

a  fixed  point,  as  X,  by  means  of     A- x 

the  hand  at  the  other  end,  as  at  % 

A.     If  the    hand   be  jerked   up-     ^^N\^    ^ 

ward,  an  apparent  movement  will 
be  transmitted  along  the  cord  like 
the  waves  on  the  sea.  If  the  hand 
be  jerked  but  once,  its  effect  will 
be  to  produce  the  crest,  A  E  N; 
the  elastic  force  of  the  cord  will 
cause  the  corresponding  hollow, 
ND  0.  The  curve,  A  END  0, 
will  advance  along  the  cord,  as- 
suming successively  the  positions 
/,  II,  III,  until  it  reaches  the  end,  X,  and  then  return  in  an 
inverted  curve,  IF,  F,  FJ,  to  the  hand.  The  curve, 
A  E  N  D  0,  is  called  a  wave. 

194.  The  particles  of  the   cord  appear  to  move  from 
one  end  of  the  cord  to  the  other.     This,  however,  is  irapos* 


FORMATION   OF  UNDULATIONS.  131 

sible;  each  particle  has  moved  only  up  and  down,  and  the 
wave  is  due  to  a  series  of  particles  which  are  passing  in  suc- 
cession from  the  highest  to  the  lowest  point  of  the  wave. 
Such  a  wave  is  called  a  progressive  undulation. 
A  0  is  the  length  of  the  wave. 
H  E  is  the  height  of  the  wave. 
D  P  is  the  depth  of  the  wave. 
HE-\-  D  P  is  the  amplitude  of  the  wave.  FlG-  115- 

A  E  N  is  called  the  phase  of  elevation  of  the  wave. 
N D  0  is  called  the  phase  of  depression  of  the  wave. 

If  a  pebble  be  dropped  in  a  placid  pool,  progressive  undu- 
lations will  be  formed.  The  waves  will  spread  in  widening 
circles  around  the  pebble,  and  decrease  in  amplitude  as  they 
increase  in  diameter,  until  they  finally  become  inappreciable. 
As  in  the  case  of  the  cord,  the  motion  of  each  particle  is 
only  up  and  down,  as  is  proved  by  the  rise  and  fall  of 
bodies  floating  upon  the  surface.  A  progressive  undulation 
is,  therefore,  only  an  advancing  form,  and  any  apparent  pro- 
gression of  the  particles  in  the  wave  is  merely  an  optical 
illusion. 

195.  The    surface  waves   of  fluids  are  propagated  by 
gravity.     All  other  waves  are   dependent,  mainly,  on  the 
elastic  force  developed  in  a  body  by  some  disturbing  force. 
Undulations  may  be  confined  to  the  body  in  which  they  are 
formed,  or  they  may  be  formed  in  one  body  and  transmitted 
through   several  others.     So   the   vibrations   of  solids   may 
cause  waves  to  be  transmitted  to  other  solids,  to  the  atmos- 
phere, or  to  water.     Any  body  through  which  waves  are 
transmitted  is  called  a  medium. 

196.  Surface  waves  have  a  crest  and  hollow,  or  an  up  and 
down    motion,    but    there    are    also    waves    in    which    the 
motion  of  the  particle  is  in  the  same  line  as  that  of  the 


132  ELEMENTS  OF  PHYSICS. 

direction  in  which  the  wave  is  transmitted.  Thus,  if  the 
piston  in  the  weight-lifter,  Fig.  102,  is  pulled  down  and  the 
pressure  suddenly  removed,  the  elasticity  of  the  air  will 


FIG.  lie. 

cause  the  piston  to  vibrate  up  and  down.  This  must  be  due 
to  the  alternate  condensation  and  rarefaction  of  the  air 
above  and  below  the  piston.  The  undulations  in  aeriform 
bodies  are  chiefly  due  to  similar  waves  of  condensation  and 
rarefaction,  in  which  the  same  particle  may  be  considered  as 
moving  backward  and  forward  instead  of  up  and  down. 

197.  Let  a  soap-bubble  containing  a  mixture  of  oxygen 
and  hydrogen  be  exploded  by  the  flame  of  a  candle.  The 
vapor  formed  by  the  union  of  these  elements  forms  a  sphere 
many  times  greater  than  the  soap-bubble,  and  thus  a  rare- 
faction will  be  produced  at  the  center  of  disturbance.  The 
pressure  of  the  surrounding  air  will  then  cause  the  vapor 


AERIAL    UNDULATIONS.  133 

sphere  to  contract,  its  elasticity  will  again  impel  it  outward, 
and  thus  it  will  continue  to  oscillate  by  alternate  refraction 
and  condensation  for  some  time. 

The  surrounding  particles  of  air  will  partake  of  these 
motions.  When  the  vapor  sphere  expands,  the  shell  of  air 
inclosing  it  will  be  condensed,  and  again  expand  as  the 
vapor  contracts.  This  aerial  shell  will,  in  like  manner,  act 
upon  a  second  aerial  shell ;  it,  in  turn,  upon  a  third,  and 
so  on. 

These  movements  are  analogous  to  the  waves  upon  the 
surface  of  liquids,  in  that  they  increase  in  circumference 
from  the  center ;  only  instead  of  a  crest  we  have  condensa- 
tion, and,  instead  of  a  hollow,  a  rarefaction.  While  a  sur- 
face wave  consists  of  a  crest  and  a  hollow ;  an  aerial  wave 
consists  of  a  condensation  and  a  rarefaction.  Fig.  116  is  an 
attempt  to  represent  to  the  eye  four  aerial  waves :  the  darker 
parts  represent  condensations,  the  lighter  the  rarefactions. 

198.  Surface  waves,  starting  from   a  center  of  disturb- 
ance, decrease  in   intensity,  because,  as   the   circles   widen, 
there  are  more  particles  to  be  moved,  and  each  will  move 
with  a  less  amplitude.     Aerial  waves   form   spherical  sur- 
faces, and,  as  they  expand,  the  number  of  particles  to  be  set 
in  motion  will  increase  as  the  squares  of  their  radii;  hence 
their  intensity  will  decrease  in  the  same  ratio — or,  the  inten- 
sity of  an  aerial  wave  diminishes  as  tlie  square  of  the  distance 
from  the  center  of  propagation  increases. 

199.  It  will  be  easily  understood  that  the  greater  the 
intensity  of  an  aerial  wave,  the  greater  will  be  the  amount 
of  condensation  and  of  rarefaction.     The  amplitude  of  an 
aerial  wave  is  the  space  through  which  any  particle  passes 
from  a  state  of  condensation  to  a  state  of  rarefaction,  and 
hence  the  amplitude  will  increase  with  the  intensity  of  the 
wave.     On  the  other  hand,  the  length  of  the  wave  will  de- 


134  ELEMENTS  OF  PHYSICS. 

pend  on  the  number  of  particles  Avhich  constitute  one  con- 
densation plus  one  rarefaction.  Hence  the  amplitude  of  a 
vibration  may  be  only  a  small  fraction  of  an  inch,  while 
the  length  of  an  undulation  may  be  many  feet. 

200.  Suppose  an  impulse  to  be  communicated  through 
one  thousand  feet  in  one  second  by  means  of  waves.  This 
will  express  the  velocity  of  the  wave  motion.  Now,  the 
greater  the  amplitude  the  greater  will  be  the  resistance  to 
be  overcome ;  the  less  the  amplitude  the  less  the  resistance, 
and,  hence,  all  the  waves  will  move  over  equal  spaces  with  equal 
velocities.  The  length  of  the  wave  depends  on  the  rapidity 
with  which  the  waves  succeed  each  other;  that  is,  on  the 
rapidity  of  the  vibrations  or  impulses  which  produce  the 
waves.  The  more  rapid  the  vibrations,  the  greater  the 
number  of  waves  and  the  shorter  the  wave  length ;  the 
slower  the  vibrations,  the  smaller  the  number  of  waves  and 
the  greater  the  wave  length.  Hence  we  may  determine  a 
wave  length  by  dividing  its  velocity  of  transmission  by  the 
number  of  vibrations  performed  in  the  same  time. 

EECAPITULATION. 

There  are  two  varieties  of  waves  : 

I.  Waves  of  crests  and  hollows,  in  which  the  direction  of  displace- 
ment is  perpendicular  to  that  of  transmission.    This  is  exemplified  by 
waves  of  water,  the  undulations  of  light  and  heat. 

II.  Waves  of  condensation  and  rarefaction,  in  which  the  direction 
of  displacement  coincides  with  that  of  transmission.     The  vibrations 
of  musical  instruments  are  transmitted  through  the  air  by  waves  of 
this  sort  to  the  ear.     These  are,  therefore,  called  sonorous  ivaves. 

The  intensity  of  a  wave  is  dependent  on  the  energy  of  the  disturb- 
ing force.  The  initial  amplitude  is  dependent  on  the  intensity. 

The  velocity  of  a  wave  is  the  rapidity  with  which  it  is  propagated 
in  a  medium. 

The  length  of  a  wave  is  dependent  both  on  the  velocity  and  the 
number  of  vibrations  in  one  second. 


CHAPTER    XIII. 

ACOUSTICS,  OR   THE   PHENOMENA    OF   SOUND. 


201.    Three  conditions  are  necessary  for  the  sensation  of 
sound  : 


Every  species  of  sound  may  be  traced  to  the  vibra- 
tions of  some  elastic  body. 

When  a  tuning-fork  sounds,  its  vibrations  may  be  felt  by 
placing  one  of  its  prongs  lightly  upon  the  teeth.  If  a  knife- 
blade  be  placed  against  the  edge  of  a  bell  that  is  ringing, 
it  will  be  made  to  rattle.  The  tremors  produced  in  the  ex- 
ternal air  by  the  vibrations  of  an  organ-pipe  are  distinctly 
perceptible.  Bodies  capable  of  producing  sound  are  called 
sonorous. 

^$Q   An  elastic  medium  is  requisite  for  the  transmission 
of  sound.     The  ordinary  medium  is  the  atmosphere. 

The  vibrations  of  sonorous  bodies  produce  in  the  air,  waves 
of  condensation  and  rarefaction,  which  correspond  in  rapidity 
and  amplitude  to  the  rapidity  and  amplitude  of  the  vibra- 
tions. These  waves  succeed  each  other  in  ever  increasing 
spheres,  until  at  last  they  reach  the  ear.  Two  or  more 
media  may  be  employed  in  transmitting  the  same  sonorous 
wave  ;  thus  persons  in  a  close  room  are  sensible  of  distant 
sounds.  In  such  a  case,  the  undulations  of  the  external  air 
cause  vibrations  in  the  windows  and  walls,  which  produce 
corresponding  undulations  in  the  air  within  the  room. 

If  a  bell,  kept  in  constant  vibration  by  clock-work,  is 
supported  on  a  thick  layer  of  loose  cotton,  under  the  re- 
ceiver of  an  air-pump,  the  sound,  at  first  distinct,  grows 

(135) 


136 


ELEMENTS  OF  PHYSICS. 


more  feeble  as  the  air  is  exhausted,  and  finally  ceases  to  be 
heard  when  a  vacuum  is  obtained.  Fig.  117.  In  like  manner 
sound  is  quenched  by  the  interpo- 
sition of  any  body  having  feeble 
elasticity.  Thus,  a  partition  filled 
with  sawdust,  or  covered  by 
a  thick  carpet,  will  prevent  the 
transmission  of  sound  from  one 
room  to  another. 
^&)  The  auditory  nerve  is  neces- 


sary to  the  sensation  of  sound. 

If  "Jie  experimenter  is  deaf,  or 
if  a  bell  rings  when  there  are  no 
hearing  organs  capable  of  per- 
ceiving the  vibrations,  they  ex- 
ist merely  as  such,  without  pro- 
ducing sensation. 
(Nevertheless,  in  studying  these 
vibrations  it  is  convenient  to  dis-  FIG.  in. 

regard  the  sensation,  and  define  sound  as  a  mode  of  motion 

which  is  capable  of  affecting  the  auditory  nerve.) 

/  '  / 

202.  \A  musical  sound  is  produced  by  vibrations  which 

succeed  each  other  at  short  and  equal  intervals.]  If  the 
vibrations  are  rapid,  the  ear  recognizes  the  sound  as  high  or 
acute ;  but,  if  slow,  as  low  or  grave.  ^ 

These  facts  may  be  shown  by  pressing  a  card  against  a 
toothed  wheel  in  motion.  Fig.  118  represents  Savart's 
wheel.  If  the  card,  E,  strikes  against  less  than  16  teeth 
per  second,  only  a  succession  of  taps  will  be  heard.  If  the 
number  exceeds  16  per  second,  the  impulses  blend  together 
in  a  clear  musical  sound.  \A.s  the  velocity  is  increased,  the 
sound  is  more  and  more  acute.  ;  Therefore///^  pitch  or  tone 
depends  on  tiie  rapidity  of  the  vibrations.  ^Savart's  wheel  has 


SAVAET'S   WHEEL. 


137 


at  H  an  apparatus  which  indicates  the  number  of  revolu- 
tions in  the  toothed  wheel  by  which  we  can  easily  calculate 
the  number  of  vibrations  per  second  that  are  required  to 


FIG.  118. 

produce  any  given  tone.  /  Sounds  are  in  unison  when  the 
rates  of  vibration  are  the  same,  j  We  may  determine  the 
rate  of  vibration  in  tuning-forks  and  other  musical  instru- 
ments by  making  the  wheel  sound  in  unison  with  them,  and 
then  noting  the  rapidity  of  the  vibrations  produced  by  it. 

If  the  vibrations  are  less  than  16  per  second,  the  ear  is 
affected  by  each  impulse  separately,  and  only  a  noise,  or  a  suc- 
cession of  noises,  is  heard,  j 

^  203.  The  quality  of  sound  depends  on  the  elasticity  and 
form  of  the  sounding  body.  Steel,  glass,  silver,  brass,  and 
cat-gut,  are  sonorous,  because  these  substances  are  highly 
elastic,  and  possess  sufficient  strength  for  rapid  vibrations. 
The  fibers  of  wool  and  cotton  are  elastic,  but  are  not  sonor- 
ous, because  their  elasticity  is  so  feeble  that  their  vibrations 
are  slow  and  inaudible.  Hence,  all  elastic  bodies  are  not 
sonorous,  although  all  sonorous  bodies  are  elastic.} 

204.    If  a  tuning-fork  be  struck  by  a  sharp  blow,  its 
sound  will   be  at  first  loud,  and   then  gradually  die  away. 
PHY*.  l-_'. 


138  ELEMENTS  OF  PHYSICS. 

The  blow  causes  vibrations  in  its  prongs  that  have  consid- 
erable amplitude;  the  greater  this  amplitude,  the  greater 
will  be  the  condensation  which  it  produces  in  the  aerial 
wave.  As  the  amplitude  decreases  the  condensation  is  less, 
until  finally  the  condensation  is  not  sufficient  to  affect  the 
ear.  QrEence,  the  intensity  or  loudness  of  the  sound  depends  on 
the  amplitude  of  the  vibrations.)  It  must  not  be  forgotten  that 
the  loudness  has  nothing  to  do  with  the  pitch  of  a  tone; 
thus,  the  same  tuning-fork  always  vibrates  with  the  same 
rapidity  and  yields  the  same  tone,  whether  that  tone  be 
loud  or  soft. 

\£he  amplitude  of  sonorous  waves  rapidly  decreases,  be- 
cause they  are  propagated  in  spherical  surfaces ;  hence,  the 
intensity  of  sound  varies  inversely  as  tJie  square  of  the  distance  of 
the  sounding  body.  J  A  drum  at  a  distance  of  one  hundred 
feet  sounds  four  times  louder  than  at  two  hundred  feet,  and 
one  hundred  times  louder  than  at  one  thousand  feet. 

205.  When  a  string  vibrates  in  free  air,  it  emits  but  a 
feeble  sound ;  but  if  it  is  fastened  to  a  violin  or  a  suitable 
sounding-box,  the  sound  is  louder.  This  arises  from  the  fact 
that  the  thin  plates  of  the  box  and  the  air  within  them  vibrate 
in  unison  with  the  string,  and  the  united  effect  is  to  produce 
a  wave  of  greater  intensity.  We  may  illustrate  this  by 
holding  a  vibrating  tuning-fork  over  the  mouth  of  a  tall  jar, 
and  carefully  pouring  water  into  the  jar.  Fig.  119.  When  it 
has  reached  a  certain  level,  the  sound  of  the  fork  will  be 
greatly  increased  by  the  vibration  of  the  column  of  air 
within  the  jar.  The  best  effect  will  be  produced  when  the 
length  of  the  air  column  is  such  that  a  wave  of  condensa- 
tion or  of  rarefaction  will  go  down  and  back  while  the 
tuning-fork  is  making  a  single  vibration.  That  is,  the 
length  of  the  column*  should  be  one-fourth  of  the  length 
of  the  sonorous  wave  produced  by  the  fork.  We  learn  from 


INTENSITY  OF  SOUND. 


139 


these  experiments  iha,t(jsound  is  increased  in  intensity  by  the 
proximity  of  a  resonant  body.} 


206.  These  experiments 
show  that  a  vibrating  body 
is  capable  of  exciting  undu- 
lations in  bodies  whose  rate 
of  vibration  is  the  same  as 
its  own.  When  the  voice 
utters  a  prolonged  loud  tone 
near  a  piano,  that  wire  will 
be  set  in  vibration  whose 
sound  is  in  unison  with  the 
voice.  Such  vibrations  are 
termed  sympathetic.  (  Only 
that  wire  answers  to  the 
voice  that  is  capable  of  emit- 
ting tfie  same  tone  when  it  is 
struck. N 


FIG.  119. 


207.  The  intensity  of  sound  depends  on  the  density  of 
the  medium  in  which  it  is  generated.     The  experiment  of 
the  bell  in  vacuo  shows  that  the  more  the  air  is  rarefied,  the 
weaker  is  the  sound.     On  the  tops  of  mountains  the  sound 
of  a  pistol  resembles  the  report  of  a  fire-cracker ;    while  a 
whisper  sounds  painfully  loud  to  the  occupants  of  a  diving- 
bell.     The   energy  with   which   solids   and  liquids  transmit 
sound  exceeds  that  of  the  atmosphere.     The  scratch  of  a  pin 
at  the  end  of  a  long  stick  of  timber  is  distinct  to  a  person 
whose  ear  is  at  the  other  end. 

208.  The   intensity  of  sound  is  weakened  in  passing 
from  one  medium  to  another.     A  noise  made  under  water 
is  feebly  heard  in  the  air,  and  vice  versa.     If  the  lungs  are 
filled  with  hydrogen,  the  voice  is  weak  and  piping.     The 


140  ELEMENTS  OF  PHYSICS. 

reason  why  sounds  are  more  distinct  by  night  than  by 
day  is  because  the  air  is  more  homogeneous.  In  the  day- 
time the  air  contains  layers  of  different  densities,  and  the 
sound  is  weakened  both  as  it  enters  and  as  it  leaves  one  of 
these  layers. 

209.  The  distance   at  which   sound  is  audible  varies 
with  the  conditions  that  determine   its  intensity.     Still  air 
of  great  density  and  uniform  temperature  is  favorable  to 
the  transmission  of  sound.     In  the  Arctic  regions,  Lieuten- 
ant Foster  conversed  with  a  sailor  at  the  distance  of  a  mile 
and  a  quarter.     The  earth  transmits  sound  further  than  air. 
The  cannonading  at  Antwerp  in  1832  was  heard  in  the  mines 
of  Saxony,  320  miles  distant. 

210.  The  velocity  of  sound.     Every  one  must  have  no- 
ticed  that   the   flash   of  a   distant   gun  is   seen   before  the 
report  is  heard.     If  the  distance  and  the  time  between  the 
flash  and  the  report  are  known,  the  velocity  of  sound  may 
be  computed.     The  velocity  of  sound  in  still  air  at  32°  F. 
is  1090  feet  per  second. 

211.  The  velocity  varies  with  the  temperature,  increas- 
ing, as  the    temperature  rises,   at  the  rate  of  1.12  feet  for 
every  degree  Fahrenheit.     At  60°  F.  sound  has  a  velocity 
of  1121  feet  per  second. 

212.  These  facts  enable  us  to  compute  the  distance  of  a 
sounding   body   when    the   time  of    transmission  is  known. 
Thus :    suppose,  on  dropping  a  stone  from  a  cliff,  eight  sec- 
onds elapse  before  the  stone  is  heard  to  strike  the  base.     A 
part  of  the   time,  x,  was  occupied  by  the  falling  body,  the 
rest,  8  —  x,   by  the  sound.      By   the  law  of  falling  bodies 
xi  x  16^  equals  the  height  of  the  cliff;   by  the  law  of  the 
transmission  of  sound  (8  —  x)  1090  also  equals  the  height. 
Hence,  x2  X  16TV— (8  — x)  1090.    x~-=  7.23;  8  —  x  =  0.77. 
The  height  of  the  cliff  is,  therefore,  839.7  feet. 


THE  VELOCITY  OF  SOUND.  141 

213.  All  sounds  are  transmitted  with  the  same  velocity 
in  the  same  medium. 

If  this  were  not  true,  the  different  notes  simultaneously 
produced  by  the  instruments  of  an  orchestra  would  reach 
the  ear  of  a  distant  auditor  one  after  another,  and  so  pro- 
duce discord. 

214.  The  velocity  of  sound  varies  with  the   medium. 
In  gases  denser  than  air,  it  moves  with  less  velocity ;    and 
in  those  rarer,  with  greater  velocity :    in  carbonic  acid,  the 
rate  is  858  feet,  and  in  hydrogen  4,164  feet  per  second.     In 
solids  and  liquids,  the  velocity  is  greater  than  in   air;    in 
water,  the  rate,  per  second,  is  4,700  feet;    in   lead,  4,030 
feet;   in  steel  and  glass,  16,600  feet ;   in  ash,  15,314  feet. 

The  difference  of  velocity  in  solids  and  in  air  may  be 
demonstrated  by  placing  the  ear  at  one  end  of  a  long  beam 
or  wall,  while  an  assistant  strikes  a  blow  at  the  other  end. 
Two  sounds  will  reach  the  ear,  the  first  through  the  solid 
and  the  other  through  the  air.  The  approach  of  a  railway 
train  may  be  soonest  heard  by  applying  the  ear  to  the 
rail. 

215.  If  the  sonorous  wave  is  not  permitted  to  expand, 
its  intensity  can   be   maintained  for  a  great  distance.     The 
speaking-tubes  employed  in  large  buildings  for  transmitting 
.messages  from  one  story  to  another  illustrate  this  fact.     The 
hearing  trumpet  concentrates  sound,  because  the  condensa- 
tion and  rarefaction  of  the  sonorous  wave  which  enters  it  is 
communicated   to    portions  of  air   which    are    smaller   and 
smaller,  and  thereby  the  intensity  is  increased. 


142  ELEMENTS  OF  PHYSICS. 


SONOROUS  WAVES. 

216.  Many  sounds  may  be   transmitted  at  the  same 
time   in   the   same  medium   without  modifying  each  other. 
A  cultivated  ear  can  readily  distinguish  the  sound  of  each 
different  kind  of  instrument  in  a  large  orchestra.     If,  how- 
ever, there  are  many  instruments  of  the  same  kind  perfectly 
in  unison,  their  sounds  will   unite   to   produce  a  resultant 
wave  of  increased  intensity.     So,  also,  many  feeble  sounds, 
separately  inaudible,  may  unite  to  produce  a  sort  of  mur- 
mur, as  is  exemplified  by  the  rustle  of  leaves,  or  the  hum 
of  a  whispering  school. 

217.  If  two  sonorous  waves  of  equal  intensity  combine, 


FIG.  120. 

the  effect  may  be  either  to  increase  or  diminish  their  inten- 
sity. We  can  readily  illustrate  this  effect  by  means  of  a 
long,  narrow  canal,  with  glass  sides,  partially  filled  with 
water.  On  tilting  one  end,  a  wave  will  pass  to  the  other 
end,  and  be  there  reflected.  If  new  waves  are  formed  by 
fresh  impulses,  we  may  so  time  the  motion  that  the  direct 
and  reflected  waves  may  be  made  to  meet  at  any  phase  of 
their  undulation.  If  crest  combine  with  crest  and  hollow  with 
hollow,  the  amplitude  of  the  resultant  wave  will  be  doubled ; 
but  if  crest  combine  with  hollow,  both  waves  will  disappear, 
and  the  surface  become  horizontal.  This  phenomenon  is 
called  the  interference  of  waves. 

In  like  manner,  if  two  sonorous  waves  of  equal  intensity 
meet  in   opposite  phases,  so  that  the  condensation  of  one 


INTERFERENCE  OF  WAVES.  143 

corresponds  with  the  rarefaction  of  the  other,  both  are  de- 
stroyed, and  silence  results.  The  feeble  sound  of  a  tuning- 
fork,  held  in  the  hand,  is  partially  due  to  the  fact  that  the 
prongs  are  vibrating  in  opposite  directions,  and  produce 
a  partial  interference  of  their  waves.  If  a  tuning-fork,  when 
vibrating,  is  turned  slowly  around  about  a  foot  from  the  ear, 
four  positions  will  be  found  in  which  the  interference  is 
total,  and  no  sound  is  heard. 

If  two  tuning-forks,  vibrating  respectively  two  hundred 
and  fifty-five  and  two  hundred  and  fifty-six  times  in  a  sec- 
ond, are  sounded  together,  they  will,  at  first,  combine  to 
produce  a  louder  sound  than  either  could  alone,  for  both 
generate  waves  in  which  condensation  corresponds  with  con- 
densation, and  rarefaction  with  rarefaction.  At  the  one 
hundred  and  twenty-eighth  vibration,  one  will  have  gained 
half  a  vibration  on  the  other,  and  their  phases  are  in  com- 
plete opposition,  and  there  will  be  no  sound,  because  the 
condensation  of  one  wave  is  neutralized  by  the  rarefaction 
of  the  other.  For  the  next  half  second,  the  interference  is 
less  and  less,  and  at  the  end  of  the  second  they  again  com- 
bine. At  every  even  number  of  half  seconds  the  sound  will 
be  doubled  in  intensity,  and  at  every  odd  number  destroyed. 

This  alternate  combination  and  interference  is  known  to 
musicians  by  the  name  of  beats.  The  number  of  beats  in 
a  second  is  always  equal  to  the  difference  in  the  two  rates  of 
vibration.  If  the  forks  vibrate  in  unison  no  beats  will  be 
heard.  If  one  vibrates  two  hundred  and  fifty  arid  the  other 
vibrates  two  hundred  and  fifty-six  times  in  a  second,  the 
number  of  beats  will  be  six. 

218.  Echoes  are  produced  by  the  reflection  of  sound  from 
distant  surfaces. 

Let  a  circular  wave  emanate  from  the  center,  0,  and 
strike  the  plane  surface,  S  B,  with  a  velocity  sufficient  to 


144 


ELEMENTS  OF  PHYSICS. 


have  carried  it  in  the  next  moment  to  S  P  B.  The  parti- 
cles in  the  perpendicular  ray,  0  0',  will  first  strike  the  sur- 
face, and  will  be  reflected  in  the  direction,  0'  P.  When  any 
diverging  rays,  as  0  D'  and 
01  reach  the  surface,  they 
will  be  reflected  on  the  other 
side  of  the  perpendiculars, 
MK  and  M'  E,  in  the  lines, 
O'D  and  0' I,  making  the  s~ 
angles  of  reflection  equal  to 
the  angles  of  incidence.  Now, 
as  the  velocities  of  the  direct 
and  the  reflected  waves  are 
the  same,  the  reflected  wave 
will  reach  the  points,  DPI,  in  the  same  time  that  the 
direct  wave  would  have  reached  D'  P  T,  and  the  same 
is  true  of  all  intermediate  points.  Hence,  the  reflected 
wave  proceeds  as  if  from  a  center,  0',  on  the  opposite  side 
of  the  surface,  SB,  and  at  a  distance  from  the  surface 
equal  to  that  of  the  center,  0,  of  the  incident  wave. 

When  the  origin  of  the  wave  is  far  distant  from  the  re- 
flecting surface,  the  waves  will  be  arcs  of  very  large  circles. 
In  such  cases,  the  diverging  rays  which  fall  upon  a  small 
surface  will  be  nearly  parallel.  Parallel  rays,  incident  upon 
a  plane  surface,  will  also  be  parallel  after  reflection. 

Echo.  The  voice  can  not  utter,  nor  the  ear  hear,  more 
than  five  syllables  in  a  second ;  therefore,  a  distinct  echo  of 
articulate  sounds  will  require  the  reflecting  surface  to  be  at 
least  1090  -r-  (5  X  2)  =  109  feet  distant,  as  the  sound  has 
both  to  go  from  and  return  to  the  speaker.  At  a  greater 
distance,  two  or  more  syllables  may  be  perfectly  repeated 
by  the  echo ;  but,  at  less  distances,  the  direct  and  reflected 
waves  will  be  more  or  less  commingled,  and  the  echo  will 
not  be  distinct. 


RESONANCE.  145 

219.  The   increased  intensity  produced  by  the    com- 
mingling of  direct  and  reflected  waves  is  termed  resonance. 
Resonance  is  specially  noticeable  in  empty  rooms  with  bare, 
smooth  walls.      If  the  echoing  walls  are  not  distant  more 
than  thirty-five  feet  from   the  speaker,  the  reflected  wave 
will  reach  the  ear  one-sixteenth  of  a  second  after  the  direct 
wave.     This  very  short  interval  will  not  be  noticed  by  the 
ear,  and   the   voice  will  be  strengthened  without  a  loss  of 
clearness.      If  the  walls  are  at  a  greater  distance  the  words 
are  less  distinct,  unless  the  echoes  are  quenched  by  the  fur- 
niture, or  by  the  presence  of  an  audience. 

220.  The  echo  may  be  heard 
when  the  direct  sound  is  inaudi-      > 
ble.      Thus,  if  two  concave   mir-    '— 
rors  are   placed  opposite  to  each 
other,    the    ticking    of    a    watch 
placed  in  the  focus  of  one  mirror 
will  be  so  reflected  that  it  may  be 

heard  in  the  focus  of  the  other,  FlG- 122- 

even  when  placed  at  a  considerable  distance.  Fig.  122. 
The  same  effect  may  be  produced  in  circular  rooms.  In 
such  a  chamber,  a  whisper  at  one  focus  will  be  heard  at  the 
other  focus,  although  inaudible  at  any  other  place.  '  Such 
whispering  galleries  are  not  uncommon.  The  dome  of  St. 
Paul's  Cathedral,  London,  and  of  the  Capitol  at  Washing- 
ton, are  fine  examples. 

221.  Sound  may  be  bent  out  of  its  course  or  refracted  in 
passing  from  one  medium  to  another.     The  laws  of  refracted 
sound  are  the  same  as  those  of  light,  and  will  be  studied 
hereafter. 


PHYS.  13. 


146  ELEMENTS  OF  PHYSICS. 

KECAPITULATION. 

10 

1.  The  quality  of  souncl  depends  on  the  elasticity  and  form  of  the 
sonorous  body. 

2.  The  pitch  of  sound  depends  on  the  rate  of  vibrations. 

3.  The  intensity  of  sound  increases:     (1.)   With  the  amplitude  of 
the   vibrations.     (2.)   With  the  density  of   the  generating   medium. 
(3.)  By  the  proximity  of  a  resonant  body. 

The  intensity  of  sound  decreases:    (1.)  As  the  square  of  the  dis- 
tance increases.     (2.)  In  passing  from  one  medium  to  another. 

The  intensity  is  maintained  or  strengthened  by  acoustic  tubes. 

4.  The   velocity   of  sound   is   not  dependent  on  quality,  pitch,  or 
intensity,  but  varies  with  the  elasticity  and  density  of  the  medium. 

(1)  may  co-exist  in  the  same  medium. 

5.  Sonorous  waves  •{  (2)  may  combine  and  interfere.  i 

(3)   may  be  reflected  or  refracted. 


MUSICAL   SOUNDS. 

222.  The   appreciation   of  musical  sounds   varies  in 
different  persons.      Some  can  hardly  distinguish   variations 
in  pitch,  although  they  are  sensible  to  variations  in  inten- 
sity.    All  ears  are  deaf  to  some  vibrations.      The  gravest 
sound  is  produced  by  16  vibrations  per  second,  the  highest 
sound  by  38,000  vibrations  per  second ;   but  there  are  many 
persons  who  can  not  hear  very  high  notes  like  the  note  of  a 
cricket,  although  they  can  distinguish  very  feeble  sounds,  as 
the  lowest  whisper. 

223.  More  than  38,000  sound  waves  are  possible,  each 
one  of  which  will,  by  itself,  produce  a  pure  tone.     No  ear  is 
capable  of  recognizing,  as  distinct  tones,  one-hundredth  part 
of  these.     Two  tones,  whose  rates  of  vibration  are  nearly 
the  same,  can  be  distinguished  from  unison  only  by  the  for- 


MUSICAL  SOUNDS.  147 

mation  of  beats.     If  these  beats  are  not  readily  perceptible, 
the  ear  recognizes  the  sound  as  the  same. 

224.   Suppose  a   guitar  string  to  be  stretched  across  a 
sounding  box,  as  in  Fig.  123.     When  the  whole  length  of 


FIG.  123. 

the  string  vibrates,  it  produces  a  sound  called  the  funda- 
mental tone  of  the  string.  Suppose  this  tone  to  be  that  due 
to  128  vibrations  in  one  second,  as  measured  by  Savart's 
wheel.  If,  now,  the  bridge,  B,  be  placed  at  half  the  length 
of  the  string,  it  will  make  256  vibrations  per  second,  or 
twice  as  many  as  the  fundamental.  If  the  string  be  again 
halved,  the  number  of  vibrations  will  be  again  doubled, 
and  so  on. 

The  ratio  between  any  two  tones  is  called  an  interval,  and 
indicates  how  much  one  sound  is  higher  than  another.  The 
interval  1  :  2  is  called  an  octave,  because,  between  any  two 
tones  bearing  this  ratio,  other  tones  may  be  placed,  so  as  to 
form,  with  the  two  extremes,  a  series  of  eight  sounds  hav- 
ing agreeable  relations  to  each  other. 

225.  These  eight  tones  constitute  the  diatonic  scale  or 
gamut.  They  are  designated  by  the  first  seven  letters  of  the 
alphabet.  If  the  length  of  the  string  which  sounds  the  fun- 
damental be  assumed  as  1,  the  relative  length  required  to 
produce  the  other  tones  are : 


148  ELEMENTS  OF  PHYSICS. 

Tones CDEFGABC 

Relative  length  of  cord.       .     .      1     I     |     |     |     f    A    i 

Relative  number  of  vibrations.     1     f     f     f     f     -f     V5     2 

The  laws  which  govern  the  vibrations  of  strings  are : 

(1)  The  number  of  vibrations  per  second  is  inversely  pro- 
portional to  the  length  of  the  string. 

(2)  The  number  of  vibrations  per  second  varies  as  the 
square  root  of  the  weight  by  which  the  string  is  stretched. 

(3)  The  number  of  vibrations  per  second  varies  inversely 
as  the  square  root  of  the  weight  of  a  given  length  of  string. 

All  these  laws  are  applied  in  the  construction  of  stringed 
instruments.  The  high  notes  on  a  piano  are  produced  by 
short,  thin  strings ;  the  low  notes  by  long  heavy  ones.  The 
strings  are  brought  to  the  proper  pitch  by  tension,  applied 
at  the  pegs. 

226.  Musicians  have  agreed  to  designate  the  tone  due  to 
128  vibrations  per  second  as  C.     It  corresponds  to  C  in  the 
second  space  of  the  base  clef.     The  number  of  vibrations 
corresponding  to  any  other  tone  may  be  found  by  multiply- 
ing this  number  by  the  fractions  -f,  f,  etc.,  which  express  the 
relative  number.     The  actual  number  employed  by  orches- 
tras in  different  cities  is  not  the  same.     For  this  reason  a 
new  scale  of  vibrations  has  been  proposed,  which  give  all 
the  tones  of  the  lower  octave  of  the  treble  in  whole  num- 
bers, C2  being  264. 

227.  The  length  of  a  sonorous  wave  is  found  by  divid- 
ing the  velocity  with  which  sound  travels  in  a  second  by  the 
number  of  vibrations   per    second.     In  air,  at  60°  F.,  the 
length  of  the  wave,  C,  is  1,121  -f- 128  =  8.7  feet. 

228.  Musical  intervals  are  named  by  the  order  of  their 
position  with  respect  to  the  fundamental,  as  seconds,  thirds, 
fourths,  etc.     The  interval  of  the  fifth,  as  CG  or  G  Z>2,  is 


MUSICAL  SCALE. 


149 


expressed  by  the  ratio  3  :  2.  The  following  table  gives  a 
condensed  summary  of  the  relations  of  two  octaves  of  the 
diatonic  scale : 


•s-m 


e- 


Hi 

MM! 

<    ! 

M'TT" 


im- 

r4iJi-4 


co  .&   o"  •*         o   S>   <M" 

tcj.-   O     >O     /%-. 

•3    .-,      N  ^  H-  co    cs    g 


si 


5    O 
:o    (N 


I    fa    fa'  -l-          «    §    C°" 

«!>-   O     ®     O 

w   S   ta"  ^H  H~  ®=   °'   °°' 


« 

^   J   <f  „,„  c^  §5  Co 

o   co   O    «IM  "    --1  ^  c0' 

rt  ^^  O  P  O 


+1       O         ^  cijoo  CO     <M     i 

^    0    0    ^          «    ^ 


t        0  o    ^     o     "     p 

I    §  I  -I  ^  ^  fe 

-  ^    o   ^  .2  «« 

:  1  l!lil 

S       S  ^   -2 

cS          ei  'S      «? 


o  ^ 

W    CQ    •< 


150  ELEMENTS  OF  PHYSICS. 

229.  The  pleasure  derived  from  music  depends  on  the 
frequent  recurrence  of  vibrations  in  the  same  phase.  Melody 
is  due  to  a  succession  of  simple  tones  having  agreeable  rela- 
tions to  each  other.  The  air  in  a  piece  of  music  is  an  ex- 


FlG.  124. 

ample  of  melody.  A  chord  is  due  to  the  simultaneous  pro- 
duction of  two  or  more  tones  in  agreeable  relations  to  each 
other.  A  harmony  is  a  melodious  succession  of  chords.  The 
air  in  music,  with  the  accompaniment,  constitutes  a  har- 
mony. 

Music  is  often  composed  and  executed  without  any  knowl- 
edge of  sonorous  waves,  because  the  ear  almost  instinctively 
recognizes  the  combinations  that  are  agreeable.  When  these 
combinations  are  analyzed,  it  is  found  that  those  are  most 
agreeable  whose  vibrations  bear  simple  relations  to  each 
other.  If  the  ratio  between  any  two  sets  of  vibrations  can 
be  expressed  by  whole  numbers  less  than  six,  the  combina- 
tion will  be  pleasant.  Such  are  notes  in  unison,  1:1;  then 
the  chords  of  the  octave,  1  :  2;*  then  follow,  in  turn,  the 
chords  of  the  fifth,  2  :  3,  the  fourth,  3  :  4,  and  so  on. 

230.  A  string  which  vibrates  transversely  along  its 
whole  length  can  be  made  to  vibrate  in  any  number  of 
segments  by  gently  touching  it  at  any  aliquot  part  of  its 
length,  as  one-half,  one-third,  etc.,  either  at  the  moment  the 


NODAL  LINES. 


151 


FIG.  125. 


string  is  set  in  motion  or  after  it  has  begun  to  vibrate.  The 
touch  quenches  the  vibration  at  the  point,  and  the  string 
divides  into  two,  three,  or 
more  segments  according 
to  the  distance  of  the 
point  touched  from  the 
end.  Now,  not  only  will 
the  vibration  cease  at  the 
point  touched,  but  also 
the  string  will  be  at  rest 
between  every  two  seg- 
ments. If  rings  of  paper 
are  placed  along  the  string 
they  will  collect  at  these 
points  of  rest,  which  are 
called  nodes.  Fig.  124. 

It  is  impossible  to  sound  the  string  as  a  whole  without,  at 
the  same  time,  producing  some  vibrations  of  its  aliquot 
parts.  The  string  will,  therefore,  yield  its  fundamental  tone 
strongly  and  some  of  its  higher  harmonics  with  less  inten- 
sity. The  same  is  true  of  other  sounding  bodies.  This  in- 
termixture of  tones  gives  each  instrument  a  peculiar  quality, 
called  timbre,  which  enables  us  to  distinguish  one  instrument 
from  another,  as  a  violin  from  a  flute. 

231.  When  plates  are  set  in  vibration  nodal  lines  are 
formed.  These  may  be  rendered  evident  to  the  eye  by  cov- 
ering the  plate  with  fine  sand.  On  quenching  the  vibration 
at  any  point,  the  sand  will  gather  at  the  positions  of  rest 
and  form  beautiful  symmetrical  figures,  as  shown  in  Fig.  125. 

If  a  thin  goblet  be  partially  filled  with  water,  and  then 
rubbed  on  the  edge  with  a  wet  finger,  the  glass  will  emit  a 
musical  tone,  and  waves  and  nodal  lines  will  be  formed  on 
the  surface  of  the  water. 


152 


ELEMENTS  OF  PHYSICS. 


232.  In  wind-instruments  the  sound  is  due  only  to  the 
column  of  air  which  is  confined 
in  the  tube.  Fig.  126  represents 
an  organ -pipe.  When  a  blast  of 
air  is  forced  through  the  aperture, 
?,  it  strikes  against  the  lip,  b,  which 
partially  obstructs  it  and  causes  the 
air  to  issue  from  b  a  in  an  intermit- 
tent manner.  In  this  way  pulsations 
are  produced,  which  cause  alternate 
condensations  and  rarefactions  within 
the  tube,  and  a  sonorous  wave  is  the 
result. 


RECAPITULATION. 


Fie;.  126. 


1.  Any  sonorous  body  gives  its  fundamental  tone  when  it  is  vibra- 
ting throughout  its  whole  length. 

2.  The  diatonic  scale  contains  eight  tones  of  different  intervals. 

3.  The  relative  number  of  vibrations  in  an  octave  is  expressed  by 
a  simple  series  of  ratios.     The  corresponding  tones  may  be  obtained 
by  -varying  the  length,  tension,  and  weight  of  strings. 

4.  The   pleasure   derived   from    music  is  due  to  a  succession   of 
melodious  or  harmonious  tones. 


CHAPTER  XIV. 

OPTICS,   OK   THE   PHENOMENA   OF  LIGHT. 

233.  ( Luminous  bodies  are  those  in  which   light '  origi- 
nates ;  all  others  are  non-luminous.    Thus,  the  sun  and  burn- 
ing bodies  are  luminous.    Trees  and  stones  are  non-1  uminous, 
but  while  the  sunlight  falls  upon  them  they  give  off  part  of 
the   light  which    they  receive,  precisely   as   if    they  were 
luminous  bodies. 

234.  ^Transparent    bodies    allow    light    to    pass    freely 
through  them.;    as  glass,  water,  air.     Opaque  bodies  do  not 
transmit  light ;  as  wood  and  the  metals.     Translucent  bodies 
transmit  light  so  imperfectly  that  objects  can  not  be  clearly 
seen  through  them ;  as  ground  glass  or  horn. 

235.  The  sun  and  the  fixed  stars  originate  the  light  by 
which  they  shine ;    the  planets  and  the  moon  shine  by  the 
light  which  they  receive  from  the  sun.     (1)    These  are  nat- 
ural sources  of  light. 

"When  any  solid  is  sufficiently  heated  it  emits  light,  and  is 
said  to  become  incandescent.  The  light  varies  with  the  inten- 
sity of  the  heat.  At  977°  F.  bodies  emit  light  of  a  dull  red 
color;  at  1,280°  F.  they  are  red-hot;  at  2,000°  F.  orange; 
at  2,130°  F.  white  hot,  and  above  this  temperature  they 
are  dazzling  white.  Hence,  any  source  of  intense  heat  will 
also  be  a  source  of  light,  if  there  are  solid  particles  present 
which  can  be  rendered  incandescent. 

(2)  ! Chemical  action  is  the  principal  source  of  artificial 
heat  aWl  of  artificial  light.  When  oxygen  and  hydrogen 
are  burned  together,  a  temperature  of  over  5,000°  F.  may 

(153) 


154  ELEMENTS  OF  PHYSICS. 

be  attained.  If  the  two  gases  alone  are  present  the  light  is 
very  feeble,  because  the  product  of  combustion  is  aeriform, 
viz.  :  the  vapor  of  water.  If,  however,  a  solid,  as  a  bit  of 
/ime,  is  held  in  the  flame,  it  becomes  incandescent,  and 
emits  a  light  of  great  intensity.  It  is  the  so-called  calcium 
OK  Drummond  light. 

\The  common  illuminating  agents,  like  oil,  tallow,  coal  gas, 
etc.,  contain  carbon  and  hydrogen.  When  these  bodies  are 
ignited,  they  are  decomposed ;  the  hydrogen  burns  with  a 
pale  flame;  into  this  flame  the  solid  carbon  particles  rise, 
become  incandescent,  and  emit  light.  They  then  burn  and 
pass  into  the  air  as  carbonic  acid.  | 

f  Besides  these  sources  of  light  ^nay  be  mentioned  (3)  me- 
chanical action,  exemplified  by  the  sparks  of  light  emitted 
when  flint  and  steel  are  struck  violently  together,  (4)  elec- 
tricity, as  in  the  glare  of  lightning,  (5)  and  the  phosphores- 
cent light  emitted  by  decaying  wood,  and  by  some  insects./ 

236.  The  phenomena  of  light  may  be  explained  by  the 
theory  that  it  is  due  to  very  small  waves  of  crests  and  hol- 
lows.   /The  wave  theory  of  light  assumes  (1)  that  matter  of 
extreme   rarity  and  elasticity,  called  the  Iwniniferous  aether, 
pervades  all  space,  even  the  interstices  between  the  molecules 
of  every  substance.     (2)   That   the   molecules  of  luminous 
bodies  are  in  a  state  of  very  rapid  vibration.     (3)   That  the 
vibrations  of  every  luminous  point  are  communicated  to  the 
aether,  and  are  then  transmitted  in  all  directions  by  spherical 
Avaves.       (4)    That    these    vibrations    or    waves    constitute 
light.) 

237.  The    velocity  of  light  was    first    ascertained    by 
Roemer  by  means  of  the  eclipses  of  the   first  moon  of  the 
planet  Jupiter.     This  moon  is  observed  to  undergo  eclipses 
by  passing  behind  the  body  of  the  planet.     Both  the  earth 
and  Jupiter  revolve  about  the  sun,  but  in  different  periods; 


VELOCITY  OF  LIGHT.  155 

consequently,  they  are  sometimes  on  the  same  side  of  the 
sun,  and  sometimes  on  opposite  sides.  In  the  former  case 
the  earth  is  the  whole  diameter  of  its  orbit,  or  about  183, 
000,000  miles  nearer  to  Jupiter  than  in  the  latter.  Now,  as 
the  moon  of  Jupiter  has  a  uniform  time  of  revolution  about 
the  planet,  its  times  of  eclipses  should  also  be  uniform  if 
light  passed  instantaneously;  but  Koemer  found  that  the 
eclipse  of  the  moon  is  seen  16ff  minutes  sooner  when  the 
earth  is  nearest  to  Jupiter  than  when  it  is  furthest  from 
him ;  therefore,  the  light  must  occupy  this  time  in  crossing 
the  earth's  orbit.  The  velocity  is  then  about  185,500  miles 
in  a  second. 

The  velocity  of  light  has  since  been  calculated  by  direct 
experiment,  and  found  to  vary  in  different  media ;  being  in 
water  144,000  miles  per  second;  in  glass,  128J30P  miles; 
in  diamond,  77,£00  miles. 

238.  Luminous  bodies  may  be  considered  as  a  collection 
of  luminous  points.  In  the  study  of  light  it  is  convenient 
to  assume,  unless  the  contrary  is  stated,  that  the  source  of 
light  is  a  luminous  point.  Suppose  we  had  a  very  small 
bit  of  incandescent  lime,  it  is  evident  that  we  could  see  it 
in  all  positions  of  the  eye  if  there  were  no  opaque  body 
intervening;  hence,  light  radiates  in  all  directions  from  a 
luminous  pointy 

A  single  line  of  light  is  called  a  ray.  A  collection  of 
rays  from  the  same  source  is  called  a  pencil  of  light.  The 
rays  of  light  emanating  from  a  point  tend  to  separate  from 
each  other,  and  thus  form  divergent  pencils ;  but,  if  the  point 
is  very  distant,  the  rays  that  enter  the  eye  will  be  sensibly 
parallel,  and,  hence,  will  form  a  pencil  of  parallel  rays  or 
a  beam  of  light.  \  Finally,  we  may  so  modify  either  divergent 
or  parallel  pencils  that  they  will  become  a  convergent  pencil, 
that  is,  one  whose  rays  are  directed  to  a  common  point! 


156 


ELEMENTS  OF  PHYSICS. 


239.  Light  moves  in  straight  lines  through  a  homoge- 
neous medium.  A  ray  of  sunlight  admitted  into  a  dark 
room  is  seen  to  be  straight  by  illuminating  the  floating 
motes  in  its  course.  When  an  opaque  body  intervenes,  the 
light  is  cut  off,  and  a  shadow  is  formed.  If  the  source  of 
light  be  a  point,  the  shadow  will  be  bounded  by  rays  tan- 
gent to  the  opaque  body.  Gen- 
erally speaking,  the  line  that 
bounds  the  shadow  is  not  clearly  FIG.  127. 

defined,   because    the    luminous    body  has   a   sensible    mag- 
nitude. 


240. 


The  intensity  of  the  light  varies  inversely  as  the 
square  of  the  distance  from  a  luminous  point)  This  is  a 
property  of  all  spherical  waves,  and  may  be  shown  experi- 
mentally for  light  by  means  of  shadows.* 

A  board  having  a  surface  one  foot  square  placed  one  foot 
from  a  very  small  candle,  will  cast  a  shadow  that  will  cover 
four  square  feet  at  double  the  distance,  nine  square  feet 
at  treble  the  distance,  and  so  on.  The  areas  increase  as  the 

square  of  the  distance,  and, 
consequently,  the  intensity  of 
light  on  each  square  inch  will 
decrease  in  proportion  to  the 
square  of  the  distance  from 
the  luminous  point. 

241.  The  relative  intensi- 
ties of  two  lights  may  be 
compared  by  an  application 
of  this  law.  Place  an  opaque 
rod  before  a  vertical  screen  of  white  paper,  and  arrange  the 
lights  so  that  each  shall  cast  a  shadow  of  the  rod  on  the 
screen.  Now  move  one  of  the  lights  backward  or  forward 
until  a  position  is  obtained  in  which  both  shadows  appear 


FIG.  128. 


RELATIVE  INTENSITY.  157 

equally  dark.  If  the  shadows  are  equal,  the  amount  of 
light  falling  on  the  screen  from  each  source  must  be  equal 
also,  hence  the  relative  intensities  of  the  two  lights  are 
found  by  squaring  the  distance  of  each  light  from  the 
screen.  In  such  measurements,  it  is  usual  to  select  a  candle 
of  known  weight  as  a  standard  unit,  the  other  light  is  then 
spoken  of  as  having  as  many  "candle-power"  as  is  expressed 
by  the  ratio  found.  The  light  which  we  receive  from  the 
sun  is  equal  to  that  of  5,563  wax  candles  placed  at  the  dis- 
tance of  one  foot.  The  light  of  the  full  moon  is  300,000 
times  less  than  that  of  the  sun. 

242.  We  should  not  forget  that  these  laws  apply  strictly 
to  luminous  points.     We  can  readily  see  that  the  illumina- 
ting effect  takes  into  account  also  the  size  of  the  luminous 
body.     Let  us  suppose,  for  example,  that  each  portion  of  a 
broad  gas  jet  shines  with  equal  intensity.     If  we  cover  the 
jet  with  a  tin  shade  having  a  narrow  slit  in  its  side,  the 
illuminating  effect  of  the  jet  will  be  decreased,  although  the 
intensity  of  the  light  which  passes  through  the  slit  will  not 
be  altered.      So,  also,  a  bright  coal-fire  may  have   as  great 
an   illuminating   effect  as    a    gas   jet,  although   with    a    less 
intensity. 

243.  \JVhen  a  pencil  of  light  falls  on  any  substance  it 
is  separated  into   parts.     (1)    Some  of  the   light   is   always 
absorbed.      (2)    Some   of  the  light   is   always   reflected.      (3) 
Some  of  the  light  may  be  transmitted.     When  the  transmit- 
ted light  is  changed  in  direction  it  is  said  to  be  refracted,  j 

Absorption.  A  very  thin  plate  of  glass  is  almost  per- 
fectly transparent,  but  if  its  thickness  is  increased,  its 
transparency  is  diminished,  and  it  may  be  made  so  thick  as 
to  transmit  no  light.  (  On  the  other  hand,  gold  may  be 
made  so  thin  that  it  wrrh  transmit  light.  The  transmitted 
light  has  a  violet-green  color.  *\ 

c/ 


158  ELEMENTS  OF  PHYSICS. 


RECAPITULATION. 

I.   Bodies  are  classified  with  reference  to  light  in  regard- 

1.  To  the  emission  of  rays:          J  Luminous. 

I  Non-luminous. 

f  Transparent. 

2.  To  the  transmission  of  rays:  \  Translucent. 

'•Opaque. 

{1.  Absorbed. 
2.  Reflected. 
3.  Transmitted. 


REFLECTION  OF  LIGHT,  OR  CATOPTRICS. 

244.  If  a  ray  of  light,  as  IB,  falls  on  a  plane  surface, 
A  C,  a  portion  of  it  will  be  reflected  or  thrown  back  in  the 
line,  E  B.     Suppose 

a  line,   P  B,  to    be 

drawn    from    the 

point    of    incidence, 

perpendicular  to  the 

reflecting  surface, 

A  C.     It  will   form 

with    the    incident 

and   reflected   rays  /       FlG-  129- 

two  angles,  viz :    IBP,  called  (the  angle  of  incidence,  and 

EBP,  called  the  angle  of  reflection,  and  in  every  case  the 

angle  of  incidence  is  equal  to  the  angle  of  reflection.  I 

245.  If  a  pencil  of  light  falls  on  a  perfectly  plane  sur- 
face, the  reflected  rays  will  proceed   in  the  same  direction, 
and  the  light  is  said  to  be  regularly  reflected.     When  a  flat 


MIRRORS.  159 

surface  is  examined  by  a  microscope  it  is  generally  found  to 
consist  of  a  number  of  minute  planes  inclined  to  each  other 
at  all  possible  angles.  Now,  as  each  little  plane  has  its  own 
perpendicular,  the  light  which  falls  on  an  uneven  surface 
will  be  reflected  in  all  directions,  and  is  then  said  to  be 
irregularly  reflected  or  diffused. 

246.  Non-luminous  bodies  are  rendered  visible  by  light 
irregularly  reflected.     The  light  which  they  reflect  renders 
them  temporarily  luminous.     Those  bodies  which  are  not  in 
the  direct  sunlight  are   illuminated   by  the    diffused   light 
reflected   from   surrounding  objects.     If  a  large  portion  of 
the  incident  light  is  reflected   regularly,  the  eye  may  per- 
ceive an  image  of  the  body  which  emits  the  light.     A  good 
mirror  gives  a  bright   image  of  objects   in   front  of  it  by 
reason  of  the  light  which  it  reflects  regularly,  but  is  itself 
seen  by  light  irregularly  reflected.     A  surface  that  reflected 
none  of  the  incident  rays  irregularly  would  itself  be  invisi- 
ble, and  no  substance  is  known  that  is  perfectly  reflecting, 
absorbing,  or  transparent. 

247.  Mirrors  are  either  plane  or  curved.     A  looking- 
glass  is  an  example  of  a  plane  mirror.     The  most  common 
kinds  of  curved  mirrors  are  those  whose  curvature  is  spher- 
ical.    A  convex  spherical  mirror  is  a  portion  of  a  spherical 
surface  reflecting  light  from  the  outer  face ;  a  concave  spher- 
ical   mirror   is   a   portion  of   a  spherical  surface  reflecting 
light  from  the  inner  face. 

The  formation  of  images  by  mirrors  may  be  determined 
by  investigating  the  images  due  to  a  series  of  points  on  the 
object. 

248.  Plane  mirrors.     Let  A  B  be  an  arrow  in  front  of 
the  plane  mirror,  MN.     Fig.  1 30.     The  point,  A,  will  emit 
a  great  number  of  rays.     One  pencil  will  be  so  reflected  that 


160  ELEMENTS  OF  PHYSICS. 

it  will  appear  to  the  eye  to  come  from  A']  a  pencil  from  B 
will  appear  to  come  from  B';  the  pencils  from  intermediate 
points  on  the  arrow  from  points  be- 
tween A'  and  B'.  Hence,  if  an  ob- 
ject be  placed  before  a  plane  mirror, 
the  image  will  be  formed  behind  the 
mirror.  Such  an  image  has  no  real 
existence,  and  it  is  called  a  virtual 
image,  because  the  rays  only  appear 
to  come  from  the  other  side  of  the 
mirror. 

In  plane  mirrors,  the  image  is  the  same  size  of  the  object, 
and  appears  as  far  behind  the  mirror  as  the  object  is  in 
front. 

249. (jlf  an  object  is  inclined  to  the  mirror,  its  image 
has  an  equal  inclination ;  hence,  the  inclination  between  the 
object  and  the  image  is  double  that  which  each  has  to  the 
mirror.  For  this  reason,  trees  appear  inverted  by  reflection 
from  the  surface  of  water.  J 

If  the  object  and  mirror  are  parallel,  there  is  a  semi- 
inversion  in  one  direction  only.  If  a  printed  page  is  held 
before  a  plane  mirror,  the  letters  are  reversed  in  a  horizon- 
tal direction,  or  from  right  to  left.  If  a  person  stands  be- 
fore a  vertical  mirror,  the  image  of  his  right  hand  will  be 
on  the  left  side  of  the  image. 

Since  the  angles  of  incidence  and  reflection  are  equal,  a 
person  may  see  his  entire  image  in  a  vertical  mirror  of  half 
his  length. 

250.  ^Miiltiple  images  are  formed  by  mirrors  inclined  to^ 
each  other./    Two  mirrors  at  right  angles  give  three  imagesj 
If  the  mirrors  are  inclined  60°,  five  images  are   produced. 
The  number  of  images  increases  as  the  angle  is  reduced, 


THE  KALEIDOSCOPE.  161 

and  would  be  infinite  when   the  mirrors  are  parallel,  if  the 


FIG.  131. 

light  were  not  gradually  weakened  at  each   successive  re- 
flection. 

251.  The  kaleidoscope  illustrates   this  property  of  in- 
clined mirrors.      It   consists  of  a  tube  containing  two  or 
three  long  and  narrow  mirrors  inclined  to  each  other ;   one 
end  of  the  tube  is  closed  by  ground  glass,  and  the  other  by 
plane  glass.     Small   colored   objects,  as  bits  of  glass,   are 
placed  in  a  cell  between  the  ground  glass  and  another  glass 
disk,  leaving  just  room   enough   for  the   objects  to  tumble 
about  as  the  tube  is  turned.     On  looking  through  the  tube, 
the  objects  and  their  images  are  seen  in  beautiful  forms. 

252.  Curved  mirrors  may  be  considered  as  made  up  of 

an  infinite  number  of  plane  mirrors 
inclined  to  each  other.  Let  TT"  be 
a  section  of  a  portion  of  a  spherical 
mirror.  C  is  called  the  center  of  curv- 
ature. The  line,  (7C",  which  passes 
through  the  vertex  of  the  mirror,  is 
called  the  principal  axis  of  the  mirror ; 


162  ELEMENTS  OF  PHYSICS. 

any  other  line,  as  C  C'  or  CC'",  which  passes  through  the 
center  of  curvature,  is  called  a  secondary  axis.  Any  radius, 
as  C/,  is  perpendicular  to  the  concave  surface,  and  its  pro- 
longation, as  J(7,  is  perpendicular  to  the  concave  surface; 
or,  what  is  the  same  thing,  these  radial  lines  are  perpen- 
dicular to  the  little  planes,  T  T ,  T  T",  of  which  we  may 
consider  the  mirror  to  be  composed. 

253.  In  concave  spherical  mirrors  the  image  formed 
on  reflection  varies  with  the  distance  of  the  object.  The 
most  important  cases  are  the  following: 

(1)    If  a  luminous  point  is  at  a  very  great  distance,  its 


FIG.  133. 

rays  will  be  sensibly  parallel.  Suppose  the  parallel  rays 
H B,  G D,  LA,  to  fall  upon  the  mirror.  Any  ray,  as  HB, 
will  be  reflected  so  that  the  angle  H  B  C  is  equal  to  the 
angle  C  B  F.  All  the  reflected  rays  will  pass  through  the 
point,  F,  which  lies  on  the  principal  axis,  about  half-way 
between  the  mirror  and  the  center  of  curvature.  This  point 
is  called  the  principal  focus  of  the  mirror. 

Now,  as  all  the  rays  are  reflected  to  one  point,  there  will 
be  a  concentration  of  light  at  the  focus,  but  no  image  will 
be  formed.  The  converse  is  also  true ;  if  a  bright  point 
were  placed  at  the  focus,  its  reflected  rays  would  be  parallel, 
and  not  enough  of  them  would  enter  the  eye  to  form  an 
image.  Hence  we  may  use  concave  mirrors  to  concentrate 
light  to  a  focus,  or,  as  in  light-houses,  to  reflect  the  rays 
from  a  lamp  placed  in  the  focus  in  parallel  rays. 


FORMATION  OF  IMAGES. 


163 


(2)  If  the  point  is  at  a  finite  distance  its  rays  will  be 
divergent.  Suppose  L  to  be  a  point  beyond  the  center  of 
curvature,  its  rays  will  converge  on  reflection  to  a  point  I, 


FIG.  134. 

between  the  principal  focus  and  the  center  of  curvature, 
and,  conversely,  rays  diverging  from  I  will  converge  on  re- 
flection to  the  point  L.  Points  so.  related  are  called  conju- 
gate foci. 

Now,  suppose  a  candle  to  be  placed  at  the  same  distance 
as  L.  The  rays  from  the  tip,  A,  will  converge  to  some 
point,  a,  on  the  secondary  axis,  A  E.  The  rays  from  B  to 


FIG.  135. 

some  point,  b,  on  the  secondary  axis,  B  L  Between  these 
two  extremes,  the  images  of  the  other  points  will  be  formed; 
hence,  a  b  is  the  complete  image  of  A  B.  The  image  is 
inverted,  smaller  than  the  object,  and  lies  beticeen  the  center 
and  the  principal  focus. 

Reflecting  telescopes  are  used  to  give  a  small  but  bright 
image  of  the  heavenly  bodies.  These  images  are  viewed 
after  being  enlarged  by  lenses.  If  a  reflecting  telescope  is 
turned  to  the  sun,  the  rays  from  any  point  on  its  surface 
will  be  parallel,  but  the  rays  from  any  two  distant  points, 
as  the  center  and  the  edge,  will  not  be  parallel.  Hence,  an 


164 


ELEMENTS  OF  PHYSICS. 


EYE 


image  of  the  sun  will  be  formed  very  near  the  principal 
focus  of  the  mirror. 

Conversely,  if  the  object  were  at  ab  the  image  would 
be  at  A  B,  enlarged,  beyond  the  center,  and  inverted,  with 
respect  to  the  object.  Both  these  images  would  be  real, 
for  either  may  be  received  on  a  screen. 

254.  (3)   When   the    object  is  between   the  principal 
focus  and  the  mirror,  a  virtual   image  is  formed,  which  is 
erect  and  enlarged. 

Let  A  B  be  an  arrow  nearer  than  the  principal  focus. 
Draw  the  axes,  c  a  and  c  b.  The  c 

pencil  from  A  will  appear  to  radiate 
from  a  in  the  same  axis,  likewise 
those  from  B  as  from  b,  and  the 
entire  image  will  lie  between  a  and 
b.  The  image  is  enlarged,  because 
the  angle  at  which  the  lines  from  a 
and  6  enter  the  eye  is  greater  than 
would  be  the  lines  proceeding  di- 
rectly from  A  and  B.  Fig.  136. 

255.  The   visual    angle   is   the 

angle  contained  between  two  lines  drawn  from  the  center  of 
the  eye  to  the  extremities  of  an  object.  (1)  For  the  same 
object,  the  angle  decreases  with  the  distance  of  the  object; 
thus,  if  the  same  object,  A  B,  is  removed  to  A'  B',  the  visual 


EYE 


B' 

} 
FIG.  137. 

angle  decreases.  Hence,  if  the  size  of  an  object  is  known, 
we  may  form  some  estimate  of  its  distance  by  its  visual 
angle,  having  learned  by  experience  to  associate  together 


SPHERICAL  MIRRORS. 


165 


N 


distance  and  angular  size.  (2)  For  the  same  distance,  the 
visual  angle  increases  with  the  size  of  the  object.  Hence, 
if  in  any  way  the  visual  angle  of  a  known  object  is  in- 
creased, it  appears  magnified,  and  if  decreased,  the  object 
appears  smaller.  The  magnifying  power  of  a  concave  mir- 
ror is  dependent,  not  on  the  area  of  its  surface,  but  upon 
its  radius  of  curvature. 

256.  In  convex  spherical  mirrors  the  images  are  always 

erect,  virtual,  and  smaller  than 
the  object.  Thus,  if  A  B  be  an 
object  at  any  finite  distance,  the 
image  of  the  point,  A,  will  be 
somewhere  on  the  axis,  A  C,  and 
B  on  the  axis,  B  C.  The  visual 
angle  will  be,  in  all  cases,  smaller 
than  would  the  angle  formed  by 
the  direct  vision  of  the  object 

AB-   Fis-138- 

257.  These  laws  are  accurate  when  the  mirror  is  a  very 
small  portion  of  a  spherical  surface.     With  a  large  portion, 
the  reflected  rays  intersect  each  other,  and  their  foci  form 
curved  lines,  which  are  called  caustics  by  reflection.     Fig.  139. 

Thus  the  heart-shaped  curve,  formed 
by  the  reflection  of  a  lighted  candle 
from  the  concave  surface  of  a  tum- 
bler containing  milk,  is  a  caustic. 
Parabolic  mirrors  are  used  for  the 
lanterns  of  locomotives,  because,  if 
a  luminous  point  is  placed  in  the 
focus  of  a  concave  parabolic  mirror, 
all  the  rays  which  strike  the  mirror  will  be  reflected  exactly 
parallel.  The  light  thus  reflected  maintains  its  intensity  for 
a  great  distance. 


C 


166  ELEMENTS  OF  PHYSICS. 

RECAPITULATION. 

Mirrors  are  either  plane  or  curved. 

{,    /  Convex. 
Spherical    i 
I  Concave, 
f  Paraboloid. 
Conical       i  _„. 
I  Ellipsoidal, 


etc. 


THE  REFRACTION  OF  LIGHT,  OR  DIOPTRICS. 

258.  When  a   pencil   of  light   falls   on   a  transparent 
body,   (1)    some  of  the  rays   are    reflected,   (2)    some    are 
absorbed,  (3)    some  are  transmitted.     When  a  ray  of  light 
passes  obliquely  from  one  medium   to  another,  it  suffers  a 
change  in  direction   which  is  called  refraction. 

259.  The  actual  occurrence  of  this  change  in  direction 
may  be  shown  by  placing  a  coin  in  an  empty  cup  in  such  a 
position  that  it  is  just  out  of  sight;    if,  now,  the  cup  be 
filled    with    water,    the 

coin  will  become  visi- 
ble, although  neither 
the  eye  nor  the  coin 
has  changed  its  posi- 
tion. Thus,  if  AB  be 
the  surface  of  the  wa- 
ter, the  ray,  m  E,  pro- 

,.         ,,  ,,  .  FIG.  140. 

ceedmg  from   the  coin, 

appears  to  come  to  the  eye  in  the  line  m'  E.  That  is,  it 
suffers  a  refraction  when  it  passes  from  the  water  into  the 
air.  Its  actual  course  is  the  bent  line  in  IE.  Fig.  140. 

260.  Suppose  an  incident  ray  of  light,  Ac,  (Fig.  141), 
moving  in  air,  to  meet  the  surface  of  water,  R  S,  and  let  c  E 
be  the  refracted  ray.    Draw  PF  perpendicular  to  the  surface 


REFRACTION.  167 

at  the  point  of  incidence,  c ;  then  A  C  P  is  the  angle  of  inci- 
dence, and  EcF  is  the  angle  of  refraction.  It  lies  between 
the  perpendicular  and  the  refracted 
ray.  If  the  incident  ray  falls  more 
obliquely,  as  a  c,  the  angle  of  re- 
fraction, ecf,  will  become  larger. 
In  order  to  compare  these  angles, 
strike  a  circle  with  any  convenient 
radius,  as  c  R,  and  draw  from  the 
points,  A,  E,  a,  e,  lines  perpendicular 
to  P  F.  These  lines  are  called  sines,  and  they  are  used  to 
measure  angles.  A  D  and  a  d  are  signs  of  the  angles  of 
incidence ;  E  F  and  ef  are  sines  of  the  angles  of  refraction. 
Now,  it  is  found  that  AD-±-EF=ad-i-ef,  or,  in  other 
words,  the  ratio-  which  exists  between  the  sines  of  the  angles 
of  incidence  and  of  refraction  is  constant  for  the  same  two 
media.  This  ratio  is  called  the  index  of  refraction;  that  is, 

. ,      .    ,         «     f      , .  sine  of  the  angle  of  incidence 

the  index  of  refraction  =  — — „    ,        -^ ^ — ? — -. 

sine  01  the  angle  ot  retraction 

If  light  passes  from  air  into  water,  the  index  of  refraction 
is  about  | ;  when  light  passes  from  water  into  air,  the  index 
of  refraction  is  the  reciprocal  of  this  fraction,  or  f. 

261.  The  index  of  refraction  varies  with  the  media. 
The  following  table  gives  the  indices  of  refraction  when 
light  passes  from  a  vacuum  into  any  of  the  substances 
named. 

Table  of  Absolute  Indices  of  Refraction. 

Vacuum    ....  1.0000  Ice 1.309 

Air 1.0003  Water 1.336 

Alcohol      ....  1.374  Bisulphide  of  Carbon  1.768 

Crown-glass    .     .     .1.534  Flint-glass        .     .     .  1.830 

Quartz  Crystal    .     .   1.548  Diamond     ....  2.439 


168  ELEMENTS  OF  PHYSICS. 

From  this  table  we  can  readily  find  the  relative  indices 
for  any  two  of  the  substances  named,  by  dividing  the  abso- 
lute index  of  one  by  the  other;  thus,  when  light  passes 
from  air  into  crown-glass,  the  index  of  refraction  is  li 


or  about  J- ;    from  crown-glass  into  air  it  is  J!s84o>  or  %' 

In  optics,  the  word  dense  signifies  of  great  refractive 
power,  and  rare,  of  little  refractive  power — without  reference 
to  the  specific  gravity  of  the  substance.  The  essential  oils 
and  alcohol  are  in  this  sense  denser  than  water,  although 
their  specific  gravity  is  less. 

262.  When  a  ray  of  light  passes  perpendicularly  from 
one  medium  to  another,  it  is  not  refracted.  If,  in  the  ex- 
periment, on  p.  166,  the  eye  is  directly  above  the  coin,  the 
coin  is  seen  in  its  true  direction,  but  there  is  also  a  curious 
effect  produced  of  making  the  coin  appear  nearer  than  it 
really  is.  This  is  due  to  the  fact  that  the  rays  which  reach 
the  eye  from  the  edge  of  the  coin  are  not  perpendicular  to 
the  surface  of  the  water,  and  hence  suffer  a  refraction. 

When  light  passes  obliquely  from  a  rarer  to  a  denser 
medium,  it  is  refracted  toward  the  perpendicular.  When 
a  star  is  near  the  horizon  it  appears  to  -be  higher  than  it 
really  is,  because,  as  its  light  passes  through  successive 
strata  of  the  atmosphere,  it  is  refracted  more  and  more,  and 
appears  in  the  direction  which  the  ray  has  when  it  enters 
the  eye. 

When  light  passes  obliquely  from  a  denser  to  a  rarer  me- 
dium, it  is  refracted  from  the  perpendicular.  In  this  case 
the  angle  of  refraction  is  always  greater  than  the  angle  of 
incidence. 

Suppose  light  to  pass  from  water  into  air.  Fig.  142.  As 
the  angle  of  the  incident  rays  I T I" ',  etc.,  increases,  the 
angle  of  the  refracted  ray,  JKR1R2,  etc.,  also  increases. 
There  will  be  found  some  ray,  as  L,  whose  angle  of  refrac- 


REFRACTION. 


169 


tion  is  a  right  angle,  and  the  ray,  if  refracted,  would  coincide 
with  the  surface.  If  the  incident 
angle  is  increased  beyond  this 
limit,  say  to  TON,  the  ray  can 
not  suffer  refraction,  but  will  be 
totally  reflected  in  the  angle,  N  0  T '. 
This  result  may  be  shown  by 
filling  a  goblet  with  water,  and 
placing  in  it  a  spoon.  When 
the  eye  is  a  little  below  the  sur- 
face of  the  water,  it  will  see  a 
bright  image  of  the  part  of  the  spoon  immersed,  reflected 
from  the  surface  of  the  water. 

REFRACTION  BY  REGULAR  SURFACES. 

263.  If  a  transparent  body  is  entirely  surrounded  by  air, 
a  ray  of  light,  on  entering  it,  will  be  refracted  toward  the 
perpendicular,  and,  on  emerging  from  the  body,  will  be 
refracted  from  the  perpendicular. 

(1)  When  the  two  surfaces  of  the  medium  are  parallel, 
the  incident  and  emergent  rays  are  also  parallel;  because 
the  ray  is  refracted  an  equal  amount  at  each  surface,  and  in 
the  opposite  direction.  The  two  refractions  do  not  cause 
any  change  in  the  general  direction  of  the  ray,  but  produce 
a  slight  lateral  displacement,  whose  amount  increases  with 

the  thickness  of  the  medium 
and  the  obliquity  of  the  in- 
cident ray.  Fig.  143. 

A  pane  of  glass  occasions 
no  distortion  of  the  objects 
seen  through  it  when  its  sides 
FIG.  143.  are  perfectly  parallel;  if  they 

are  not  parallel,  the  objects  will   appear  more  or  less  dis- 
torted. 

PHYS.  15. 


170 


ELEMENTS  OF  PHYSICS. 


(2)  A  prism  is  a  transparent  medium  having  two  plane 
surfaces  not  parallel.     A  prism  may  be  a  solid  wedge  of 
glass  or  crystal,  or  may  consist  of  liquids  inclosed  in  hollow 
prisms  with  sides  of  plane  glass.     The  path  of  light  through 
a  prism  is  exhibited  in  Fig.   144. 

Suppose  the  light  to  come  from  0. 

As   the   incident  ray,  0  D,  enters 

the  prism,  it  is  refracted  towards  /     ?' 

the  perpendicular,  P  P,  because  it 

enters  a  denser  medium,  and  will  FlG-  144> 

proceed  in  the  line  D  K.     On  leaving  the  prism  for  a  rarer 

medium,  it  will  be  refracted  from  the  perpendicular,  P'  P", 

and  will  emerge  -in  the  line  K H.     The  light  is  thus  twice 

refracted   toward  the   base  of  the  prism,  and   the   eye  which 

receives  the  emergent  ray,  K  H,  sees  the  object  at  Of  nearer 

the    summit    of   the    prism   than    the  real  position    of   the 

point,  0. 

(3)  A  lens  is  a  transparent  medium,  having  at  least  one 
curved  surface.     The   curved  surface   is   usually  spherical. 

ABC  D         E         F 


FlG.  145. 

There  are  six  .  varieties  of  spherical  lenses,  viz. :  A  is  a 
double  convex,  B  a  plano-convex,  C  is  a  meniscus,  concave  on 
one  side  and  convex  on  the  other,  the  convex  surface  hav- 
ing the  shorter  radius.  These  three  are  thickest  at  the 
center,  and  are  converging  lenses.  D  is  a  double  concave,  E  is 
a  plano-concave,  and  F  is  a  concavo-convex,  the  concave  sur- 
face having  the  shorter  radius.  These  three  are  thinnest  at 
the  center,  and  are  diverging  lenses.  Fig.  145. 


DOUBLE  CONVEX  LENSES. 


Ill 


The  line,  MN,  which  passes  through  a  lens  perpendicular 
to  both  surfaces,  is  called  the  axis  of  the  lens.  The  double 
convex  lens  may  be  regarded  as  a  series  of  prisms  whose 
bases  are  turned  toward  the  axis,  and  the  double  concave 
lens  as  a  series  of  prisms  whose  bases  are  turned  away 
from  the  axis.  If  the  sides  of  each  prism  are  infinitely 
small,  the  series  will  form  a  spherical  surface.  Hence,  as  a 
prism  refracts  light  toward  its  base,  a  convex  lens  will  re- 
fract the  light  toward  its  axis,  and  tend  to  converge  the 
rays ;  a  concave  lens  will  refract  light  away  from  its  axis, 
or  tend  to  disperse  the  rays.  We  shall  study  only  the 
double  convex  and  the  double  concave  lenses,  because  the 
properties  of  these  lenses  are  similar  to  the  others  of  the 
same  group. 

264.  If  parallel  rays  fall  upon  a  convex  lens,  the  rays 
will  converge  to  one  point, 

which  is  called  the  princi- 
pal focus  of  the  lens.  This 
focus  is  real,  for  all  the 

rays  of  the  sun  may  be       

collected  at  this  point. 
The  ordinary  burning- 
glass  is  simply  a  large  double  convex  lens.  Fig.  146. 

265.  If  the  rays  diverge  from  the  principal  focus  they 
will  be  rendered  parallel.     A  lamp  so  placed  will  illuminate 
objects  at  a  great  distance.     Fig.  146. 

8 


FIG.  146. 


FIG.  147. 

266.   If  the  rays  diverge  from  a  point  beyond  the  prin- 


172 


ELEMENTS  OF  PHYSICS. 


cipal  focus,  as  at  I,  they  will  converge  on  refraction  to  some 
point,  as  L,  also  at  a  greater  distance  than  the  principal 
focus ;  and  conversely  if  they  diverge  from  L  they  will 
converge  at  L  Both  these  foci  are  real ;  one  is  less  than 
twice  the  principal  focal  distance  and  the  other  greater. 

267.  Real  images  are  formed  when  the  object  is  at  a 
finite  distance  beyond  the  principal  focus.  Suppose  A  B  to 
be  at  more  than  twice  the  principal  focal  distance.  A  ray 
diverging  from  A  will  converge  on  refraction  at  a ;  diverging 


FIG.  148. 

from  B,  at  b.  Hence,  the  image  of  A  B  will  be  a  b,  real, 
inverted  and  smaller  than  its  object.  Conversely,  if  a  b  were  a 
luminous  object  at  less  than  twice  the  principal  focal  distance, 
but  beyond  the  focus,  its  image  would  be  A  B,  real,  inverted, 
and  larger  than  the  object. 

If  the  rays  diverge  from  a  point  nearer  the  lens  than 


...-n 


FIG.  149. 

the  principal  focal  distance  they  will  be  less  divergent  on 
refraction,  but  will  form  no  real  focus,  nor  even  be  rendered 
parallel.  Thus,  the  rays  from  L  will  appear  to  come  from 
a  virtual  focus  at  I,  which  is  on  the  same  side  of  the  lens  as 


DOUBLE  CONCAVE  LENSES. 


173 


the  luminous  point.     If  a  small  object,  as  A  E,  (Fig.  150), 
were  so  placed,   a  virtual  image  would  be  formed  at  a  6, 


A 


FIG.  150. 

which  would  be  erect,  and   larger  than  the  object.     This  is 

the  ordinary  way  of  using  a  lens  as  a  magnifying  glass. 
268.  The  foci  of  concave  lenses  are  always  virtual,  and 

the  images  formed  by  them  are  also  virtual.     Let  A  B  be 

an  object  in  front  of  a  con- 
cave lens.  The  rays  from 
the  point,  A,  will  be  so  re- 
fracted as  to  appear  to  come 
from  its  virtual  focus,  a,  and 
the  rays  from  the  point,  J?, 
will  appear  to  diverge  from 
FIG- ia-  its  focus,  b.  Therefore,  the 

eye  sees  at  a  b  an  image  of  A  B,  which  is  always  virtual, 

erect,  and  smaller  than  the  object. 


FIG.  152. 


269,   If  a  crystal  of  Iceland  spar  be  placed  upon  an 
object,  as  in  Fig.  152,  a  double  image  will  be  perceived. 


174  ELEMENTS  OF  PHYSICS. 

This  phenomenon  is  called  double  refraction.  Most  transpar- 
ent bodies  have  the  same  property  of  refracting  light  in 
two  separate  pencils,  but  not  to  so  great  a  degree. 

These  doubly  refracted  rays  have  properties  which  dis- 
tinguish them  from  ordinary  rays,  and  are  said  to  be  polar- 
ized. Light  is  also  polarized  by  absorption,  single  refraction, 
and  reflection.  The  subject  of  polarized  light  is  so  abstruse 
that  it  can  not  be  taken  up  with  profit  in  an  elementary 
course.  It  must  suffice  us  to  say  that  when  a  ray  has  been 
polarized,  it  will  neither  be  reflected,  refracted,  nor  absorbed 
in  precisely  the  same  manner  as  common  light,  although  the 
eye  can  not,  unaided,  distinguish  one  from  the  other. 

RECAPITULATION. 

I.  Light  is  not  refracted : 

1.  In  passing  through  a  uniform  medium,  nor 

2.  When  passing  perpendicularly  from  one  medium  to  another. 

II.  Light  is  refracted  in  passing  obliquely  into  a  second  medium : 

1.  Toward  the  perpendicular,  when   the   second  is  the  denser. 

2.  From  the  perpendicular,  when  the  second  is  the  rarer. 

III.  Lenses  are  either  converging  or  diverging. 

IV.  The  effects  of  concave  mirrors  and  of  convex  lenses  are  simi- 
lar :     When  the  object  is 

1.  Nearer  than  the  principal  focal  distance, 
The  image  is  virtual,  erect,  and  magnified. 

2.  At  the  principal  focus 

There  is  dispersion  of  light  in  parallel  rays. 

3.  Beyond  the  principal  focus,  but  less  than  twice  its  distance, 
The  image  is  real,  inverted,  and  magnified. 

4.  At  twice  the  principal  focal  distance, 

The  image  is  real,  inverted,  and  of  equal  size. 


CAMERA   OBSCURA. 


175 


5.  At  a  finite  distance,  more  than   twice   the   principal   focal 
distance, 

The  image  is  real,  inverted,  and  diminished. 

6.  At  an  infinite  distance, 

There  is  concentration  of  light  at  the  principal  focus. 

V.  The  effects  of  convex  mirrors  and  of  concave  lenses  are  also 
similar,  forming  images  which  are  always  virtual,  erect,  and  smaller 
than  the  object. 


OPTICAL  INSTRUMENTS,  AND  VISION. 

270.   If  luminous  rays  are  transmitted  through  a  small 
aperture,  and  there  received  on  a  white  screen,  they  form  in- 


FlG.  153. 

verted  images  of  external  objects.  The  luminous  rays  pro- 
ceed in  straight  lines ;  those  from  the  top  of  the  object,  (Fig. 
153),  are  received  on  the  bottom  of  the  screen,  and  those 
from  the  base  of  the  object  on  the  top  of  the  screen.  The 
rays  of  light  must,  therefore,  cross  each  other  without  inter- 
fering. A  darkened  room  so  arranged  is  one  form  of  the 
camera  obscura. 


176  ELEMENTS  OF  PHYSICS. 

The  photographer's  camera,  Fig.  154,  differs  from  this  only 

A 


FIG.  154. 


in  having  a  convex  lens  in  the  tube,  A.  The  effect  of  the 
lens  is  to  converge  the  rays  so  as  to  produce  a  small  image 
of  the  object,  which  is,  at  the  same  time,  clear  and  well 
defined. 

271.   The  mechanical  action  of  the  eye  is  very  similar 
to  that  of  the  photographer's  camera.    The  human  eye  is  very 


FIG.  155. 

nearly  spherical,  and  is  about  an  inch  in  diameter.  It  con- 
sists essentially  of  (1)  three  enveloping  coats  and  (2)  three 
refracting  bodies.  Fig.  155  presents  these  parts  in  hori- 
zontal section. 


THE  HUMAN  EYE.  177 

(1)  The  outer  coat,  or  white  of  the  eye,  is  a  tough  and 
opaque  membrane  called  the  sclerotic.     In  the  front  part  of 
this,  the  transparent  cornea,  a,  is  set  in  like  a  watch-glass. 

The  middle  coat,  k,  is  the  choroid,  which  consists  of  a 
membrane,  abundantly  supplied  with  blood-vessels,  and  cov- 
ered, on  its  inner  face,  by  a  dark,  velvety  substance,  called 
the  black  pigment. 

The  inner  coat  is  the  retina,  m,  which  is  mainly  an  expan- 
sion of  the  optic  nerve,  n,  with  the  addition  of  terminal 
nerve  elements  for  the  perception  of  light,  spread  out  in 
very  fine  net-work  on  the  black  pigment. 

Near  the  junction  of  the  cornea  and  sclerotic,  the  choroid 
becomes  thicker,  and  terminates  in  the  ciliary  processes.  To 
the  outer  portion  of  these  is  attached  an  opaque,  contractile 
membrane,  d,  called  the  iris,  because  it  is  the  colored  por- 
tion of  the  eye.  The  iris  is  pierced  by  an  aperture,  called 
the  pupil,  through  which  the  luminous  rays  pass  to  the 
bottom  of  the  eye. 

(2)  Behind  the  iris,  and  supported  by  a  suspensory  liga- 
ment, attached  to  the  ciliary  muscle  which  proceeds  from 
the   ciliary   processes,   is   the  crystalline   lens,  f.      This   is   a 
double   convex  lens,  having  its  anterior  face  of  less  con- 
vexity than  the  posterior. 

The  portion  of  the  eye,  e,  between  the  cornea  and  the 
crystalline,  is  filled  with  a  thin  liquid,  called  the  aqueous 
liwnor. 

Behind  the  crystalline  is  the  chamber,  h,  which  is  filled 
with  a  jelly-like  liquid,  called  the  vitreous  humor.  The 
humors  and  the  crystalline  are  each  surrounded  by  a  deli- 
cate membrane,  or  capsule. 

If  a  luminous  point  be  placed  before  the  eye,  the  central 
rays  pass  through  the  cornea  and  enter  the  aqueous  humor. 
Of  these  rays,  the  more  divergent  are  cut  off  by  the  iris, 


178  ELEMENTS  OF  PHYSICS. 

and  only  those  that  are  nearly  parallel  are  admitted  through 
the  pupil.  These  are  transmitted  through  the  crystalline 
and  the  vitreous  humor,  arid  finally  fall  upon  the  retina. 
The  effect  of  these  refracting  bodies  is  to  form  at,  or 
very  near,  the  retina  an  image  of  the  luminous  point. 
The  same  being  true  of  all  diverging  pencils  proceeding 
from  an  object,  there  will  be  formed  on  the  retina  a  small 
inverted  image  of  the  object. 

272.  The  sensation  of  sight  is  due  to  the  impression 
made  by  the  image  on   the  terminal  percipient  nerve  ele- 
ments of  the.  retina,  and  thence  conveyed  by  the  optic  nerve 
fibers  to  the  brain.     These  nerve  elements  are  contained  in 
a  layer  next  the  black  pigment,  and  consist  of  a  great  num- 
ber of  very  minute  bodies,  arranged  side  by  side,  and  re- 
sembling   rods   and   cones,  standing    perpendicularly  to    the 
surface  of  the   retina.     It  is   supposed  that  the  waves  of 
light  falling  upon  this  layer  of  rods  and  cones  produce  vibra- 
tions, which  are  conducted  by  the  nerve  fibers  in  such  a  way 
to  the  brain  that  it  is  excited  and  acknowledges  the  recep- 
tion of  the  luminous  image  on  the  retina. 

273.  The  impression  made  on  the  retina  is  not  instan- 
taneous, and  when  once  made  continues,  on  the  average,  for 
nearly  one-third  of  a  second  after  the  exciting  cause  has 
ceased   to   act.     If,   therefore,   an   ignited   coal    be  whirled 
about  rapidly,  luminous  rings  are  produced. 

Many  optical  toys  owe  their 
effect  to  the  duration  of  the 
impression  on  the  retina.  The 
Thaurnatrope,  Fig.  156,  con- 
sists of  a  card  which  is  made 
to  revolve  by  means  of  strings  G.  isc. 

attached  to  its  sides.      A  horse  may  be  so  painted  on  one 


VISION.  179 

side  and  a  rider  on  the  other,  that  a  rapid  revolution  of  the 
card  will  cause  the  rider  to  appear  seated  on  the  horse. 

274.  The  accommodation  of  the  eye  to  different  dis- 
tances is  effected  by  the  action  of  the  ciliary  muscle  upon 
the  crystalline  lens.     When  the  eye  is  turned  toward  a  dis- 
tant object,  the  muscle  relaxes  and  the  lens  is  flattened ;  but, 
for  near  objects,  the  muscle  contracts  and  the  lens  becomes 
more  convex.     In  this  way  the  conjugate  focus  of  the  object 
is  made  always  to  fall  upon  the  retina.     The  power  of  ac- 
commodation   is  very  great,   and   is  exerted   unconsciously 
with  marvelous  rapidity.     Nevertheless,  there  is,  for  all  eyes, 
a  certain  distance  at  which  the  parts  of  an  object,  as  the 
letters  on  this  page,  are  seen  most  distinctly.     This  distance, 
which,  for  ordinary  eyes,  varies  from  five  to  ten  inches,  is 
called  the  distance  of  distinct  vision. 

275.  Par-sighted  eyes  are  those  whose  nearest  point  of 
distinct  vision  exceeds  ten  inches,  and  near-sighted  eyes  are 
those  whose  farthest  point  of  distinct  vision  is  a  short  dis- 
tance, varying  from  three  inches  to  twenty  feet.     For  normal 
eyes,  the  farthest  point  of  distinct  vision  is  infinitely  distant, 
the  nearest  point  more  than  three  inches. 

276.  An  object  will  not  appear  distinct  to  the  normal 
eye  unless   the  rays  which  proceed  from  it  enter  the  eye 
nearly  parallel.     This  will  be  the  case  for  a  luminous  point 
when  it  is  distant  more  than  eighteen  inches.     If  a  printed 
page  be  brought  too  close  to  the  eye,  the  letters  appear  more 
or  less  blurred,  because  the  rays  are  too  divergent  to  focus 
on  the  retina.     Now,  place  between  the  eye  and  the  page  a 
thin  card  in  which  a  pin-hole  has  been  pricked.     The  card 
will  exclude  the  outer  divergent  rays,  and  the  eye  will  be 
able  to  converge   the   few  nearly  parallel   rays   which   pass 
through  the  pin-hole  upon  the  retina,  and  thereby  form  a 


180  ELEMENTS  OF  PHYSICS. 

faint,  but  distinct,  image.    At  the  same  time,  the  letters  will 
appear  magnified,  because  the  visual  angle  is  increased. 

277.  A  convex  lens  placed  a  little  nearer  an  object  than 
its  focal  distance  will  converge  all  its  rays  upon  the  retina, 
thus   preserving  all  the  light  while  it  magnifies  the  object 
by  increasing  its  visual  angle.     With   a  powerful  lens  the 
object   must  be  very  near   the   lens,  and,  consequently,  the 

field  of  view  will  be  very  small.  The  magnifying  glasses  used 
for  viewing  pictures  magnify  but  little,  because  their  radius 
of  curvature  is  very  large,  but  they  afford  a  large  field  of 
view.  Pocket  microscopes  usually  contain  two  or  three  convex 
lenses,  acting  as  a  single  thick  lens.  They  seldom  magnify 
more  than  five  diameters. 

278.  The  compound  microscope  consists  of  an  object- 
glass,  M,  of  short  focus,  and  an  eye-glass,  N,  of  less  magni^ 
fying  power.     The  object,  A  B,  is  placed  a  little  beyond  the 

M 


focus  of  the  object-glass,  and  its  real  image,  a  6,  inverted  and 
magnified,  is  formed  a  little  within  the  focus  of  the  eye-glass. 
By  this  glass  the  real  image  is  viewed  as  with  a  simple 
microscope,  and,  hence,  forms  another  image,  a'  b',  which  is 
still  more  magnified,  and  is  virtual.  The  advantage  of  this 
form  of  microscope  is  that  a  high  magnifying  power  is  ob- 
tained with  a  comparatively  large  field  of  view. 

The  difference  between  the  simple  and  compound  micro- 
scopes consists  in  this,  that  in  the  simple  microscope  the 
object  is  viewed  directly,  and  in  the  compound  microscope  a 
real  magnified  image  of  the  object  is  viewed  with  a  common 
magnifier. 


THE  TELESCOPE. 


181 


279.  The  telescope  is  used  for  viewing  distant  objects. 
In  refracting  telescopes  a  real  image  is  formed  by  an  object- 
glass  of  small   convexity ;    in   reflecting    telescopes    a    real 
image  is  formed  by  a  concave  mirror  ;    these  images  are,  in 
both   cases,   very  small,  but   very   bright.     They  are   then 
viewed  by  an  eye-glass  of  high  magnifying  power. 

280.  The    astronomical   refracting  telescope   consists 
of  the  object-glass,  M,  and  the  eye-glass,  N.    Fig.  158.    The 
object-glass  forms  an  inverted  image,  b  a,  of  a  distant  object, 


FIG.  158. 

A  B,  in  its  principal  focus,  F.  This  image  is  then  viewed 
by  the  eye-glass,  JV,  which  is  so  placed  as  to  receive  the 
image  at  a  distance  a  little  less  than  its  own  focal  length. 
The  image  is  inverted.  This  occasions  little  inconvenience 
in  viewing  heavenly  bodies,  but  would  be  a  serious  defect 
if  employed  for  terrestrial  objects. 

281.   The  terrestrial  telescope  has,  therefore,  two  addi- 
tional lenses  for  rendering  the  image  erect.     Fig.  159.     The 


A  M, 


FIG.  159. 


action  of  these  glasses,  P  and  Q,  will  be  understood  by 
tracing  the  rays  from  the  luminous  point,  A.  P  renders  them 
parallel,  and  gives  them  a  new  direction.  Q  converges  them 
in  the  focus  of  the  eye-glass,  so  as  to  form  a  real  image 
which  has  the  same  position  as  the  object.  This  second 


182  ELEMENTS  OF  PHYSICS. 

image  is  then  viewed  in  the  ordinary  way  by  the  eye-glass, 
R. 

282.    Reflecting  telescopes  have  several  different  forms. 
Herschel's  telescope  is  represented  in  Fig.  160.     It  consists 


•       ,. o 

FIG.  160. 

of  a  concave  reflector,  M,  and  a  convex  lens,  0.  The 
reflector  is  so  inclined  to  the  axis  of  the  tube  that  the 
image  of  the  star  is  formed  near  the  side  of  the  tube,  in 
front  of  the  eye-piece,  0,  and  is  then  magnified  by  the  lens 
and  received  by  the  eye. 

Lord  Rosse's  telescope  has  a  mirror  six  feet  in  diameter. 
The  amount  of  available  light  received  at  the  eye-piece 
exceeds  250,000  times  as  much  light  as  commonly  enters 
the  eye.  This  enormous  illuminating  power  enables  the 
observer  to  use  eye-glasses  whose  magnifying  power  is  6,000 
diameters.  This  would  render  an  object  as  large  as  the 
capitol  at  Washington  visible  at  the  distance  of  the  moon. 

Alvan  Clarke,  of  Boston,  has  lately  succeeded  in  making  a 
refracting  telescope  for  the  Washington  observatory,  whose 
object-glass  is  26  inches  in  diameter. 

283.  The  magic  lantern  is  an  instrument  by  which 
translucent  objects  are  magnified  and  thrown  on  a  screen. 
Fig.  161.  A  lamp  is  placed  in  the  common  focus  of  a 
reflector,  M  N,  and  of  a  convex  lens,  A,  so  that  a  strong 
beam  of  light  is  thrown  on  the  object  which  is  inserted  in 


THE  STEREOSCOPE. 


183 


the  slit,  CD.  A  magnifying  lens  at  B  forms  an  image  of 
the  object  on  the  screen,  EF.  The  objects  are  usually  painted 
on  glass,  but  the  instrument  may  also  be  used  to  magnify 
any  translucent  object. 


FIG.  id. 

The  solar  microscope  is  essentially  a  magic  lantern  illumi- 
nated by  the  sun. 

284.  The  stereoscope.  If  a  solid  object,  as  a  die,  be 
held  a  short  distance  before  the  eyes,  each  eye  will  see  the 
object  from  a  different  point  of  view;  and.  consequently, 


• 


FIG.  162. 

the  two  images  formed  on  the  retina  will  not  be  exactly 
•alike.  Fig.  162  represents  a  die  as  seen  by  the  left  and 
right  eyes  respectively.  By  the  blending  of  these  two 
images,  the  object  appears  solid.  This  effect  will  be  pro- 
duced in  the  engraving,  if  a  card  be  held  between  the  two 
figures,  and  they  are  steadily  looked  at  for  a  few  seconds, 
one  by  the  right  eye  and  the  other  by  the  left.  The  stereo- 
scope, Fig.  163,  is  contrived  to  assist  the  eye  in  blending 
two  slightly  different  pictures  of  the  same  object,  taken 


184 


ELEMENTS  OF  PHYSICS. 


from  points  of  view  related  to  each  other  in  the  same  man- 
ner as  the  two  eyes  of  the  observer.  These  pictures  are 
placed  in  the  bottom  of  a  box  and  viewed 
through  two  eye-pieces,  which  are  segments 
cut  from  a  double  convex  lens.  A  dia- 
phragm,  D,  (Fig.  164),  prevents  each  eye 


B 


FIG.  1G4. 


FIG.  163. 

from  seeing  more  than  one  picture.  The  rays  of  light  from 
A  after  emerging  from  the  lens,  M,  reach  the  eye  as  if  they 
came  from  0,  and  the  rays  from  the  lens,  N,  also  appear  to 
come  from  C.  Thus,  the  two  pictures  are  blended  in  one, 
and  appear  to  come  from  a  solid  object  at  C. 


RECAPITULATION. 


Enveloping 
coats. 

C  Sclerotic, 
•j   Choroid. 
(.  Retina. 

Refracting 
bodies. 

(  Aqueous  humor 
I   Crystalline  lens. 
(  Vitreous  humor. 

I.  The  human  eye 
consists  of 


II.  The  sensation   of  sight   is   produced  by  luminous  vibrations 
passing  through  the  cornea,  aqueous   humor,  pupil,  crystalline  lens, 
vitreous  humor   to   the   retina,  and  there   exciting,  in  the  layer  of 
rods  and  cones,  vibrations  which  are  conveyed   by  the  optic  nerve 
fibers  to  the  brain. 

III.  All   optical   instruments  are   combinations  of  either  prisms, 
lenses,  or  mirrors. 


CHROMATICS. 


185 


IV-   Microscopes  are  used  for  magnifying  near  objects. 
Telescopes  are  used  for  magnifying  distant  objects. 

V.    Microscopes  are  simple,  and  compound. 
Telescopes  are  refracting,  and  reflecting. 


CHROMATICS,  OR  COLORS. 

285.  If  a  pencil  of  solar  light  be  admitted  into  a 
darkened  room  through  a  very  small  aperture,  it  will  form 
a  round,  white  image  of  the  sun,  as  represented  at  K,  (Fig. 
165).  If,  now,  a  prism  be  placed  in  the  path  of  the  pencil, 
it  will  form  on  a  screen  an  elongated  band  of  colors,  which 


FIG.  165. 

is  called  the  solar  spectrum.  That  is,  the  prism  not  merely 
refracts  the  rays,  but  refracts  them  unequally,  and  produces 
what  is  called  the  dispersion  of  light.  Newton  distinguished 
seven  of  these  colors  as  primary,  which  are,  beginning  with 
the  least  refracted,  red,  orange,  yellow,  green,  blue,  indigo, 
violet. 

286.   White  solar  light  is,  therefore,  composed  of  differ- 
ent colored  rays.    An  additional  proof  of  this  is  found  in  the 
PHYS.  16. 


186 


ELEMENTS  OF  PHYSICS. 


fact   that,  when  all  the  colors  of  the  spectrum  are  recono- 
bined,  they  will  reproduce  white  light.      Thus,  if  all  the 


FIG.  166. 

rays  of  the  spectrum  are  received  on  a  convex  lens  or  on  a 
concave  mirror,  a  white  image  will  be  formed  in  the  focus. 
If  a  circular  card  be  painted  with  the  seven  colors  and 
revolved  rapidly,  it  will  appear  of  a  white  color,  more  or 
less  pure  according  as  the  colors  on  the  card  more  or  less 
exactly  imitate  those  of  the  spectrum.  Fig.  166. 

287.   If  the  solar  light  be   admitted  through    a   very 


A 

JJ. 

f 

, 

G 

• 

J.IJ       J 

0 

OAKK  HEAT  KAYS 


CHEM/CAL    KAYS 


FIG.  167. 


narrow  slit  and  received  on  a  good  flint-glass  prism,  it  will 


FRAUNHOFEES  LINES.  .187 

be  found  that  the  colors  of  the  spectrum  are  not  continuous, 
but  that  they  are  interrupted  by  numerous  dark  spaces, 
known  as  Fraunhofer's  lines.  On  viewing  the  spectrum 
with  a  telescope  two  thousand  of  these  lines  are  visible. 
Seven  are  more  distinct  than  the  rest,  and  are  designated 
by  the  letters  B,  C,  D,  E,  F,  G,  H,  to  serve  as  means  of 
reference.  Fig.  167. 

288.  The  index  of  refraction  for  the  different  colors  is 
fixed  with  precision  by  ascertaining  the  position  of  Fraun- 
hofer's lines,  B,  C,  etc.    The  table  on  p.  167  gives  the  index 
of  refraction  for  the   line  E  in   the  yellowish -green   rays, 
which  is  assumed  as  the  mean  of  all  the  rays.     If  similar 
prisms  are  made  of  different  substances  the  mean  refraction 
may  be  very  nearly  the  same,  and  yet  the  spectra  they  fur- 
nish be  of  very  unequal  lengths.     The  dispersive  power  of  a 
medium  indicates  the  amount  of  separation  it  produces  in 
the  extreme  rays  compared  with  the  amount  of  refraction 
in  the  mean  rays. 

Table  of  Dispersive  Powers. 

Bisulphide  of  Carbon  0.130  Crown-glass  .  .  .  0.036 
Flint-glass  ....  0.052  Water  ....  0.035 
Diamond  ....  0.038  Quartz  crystal  .  .  0.026 

289.  If  two  prisms,  exactly  alike,  are  placed  near  each 
other,  with   their  bases  turned  in   a 

contrary  direction,  the  one  will  ex- 
actly neutralize  the  other,  and  the 
light  will  emerge  from  the  second  as 
if  from  a  medium  with  parallel  faces. 
Now,  suppose  two  unequal  prisms,  one 
of  flint  and  the  other  of  crown-glass,* 

be  placed  together,  as  in  Fig.  168.  The  dispersive  power 
of  flint-glass  is  almost  double  that  of  crown-glass,  while 


188  ELEMENTS  OF  PHYSICS. 

its  refractive  power  is  but  little  greater ;  hence,  if  the  refract- 
ing angle  of  the  former  is  made  so  much  smaller  than  the 
latter  that  their  dispersive  powers  are  equal,  only  white 
light  will  emerge,  but  it  will  be  refracted  with  about  half 
the  refracting  power  of  a  single  prism  of  crown-glass. 

An  achromatic  lens  is  made  on  the  same  principle  by 
combining  a  double  convex  lens  of  crown-glass 
with  a  concavo-convex  lens  of  flint-glass.  Fig. 
169.  Such  a  lens  transmits  un colored  light.  In 
any  single  lens,  the  image  is  fringed  with  colored 
rays,  which  are  due  to  the  dispersive  power  of 
the  lens. 

290.  The  spectra  formed  by  artificial  lights  are  usually 
wanting  in  several  colors,  but  yield  the  remainder  with  the 
same  refrangibility  as  the  corresponding  colors  of  the  solar 
spectrum.      An    almost    colorless    flame    may   be    produced 
by  burning  pure  alcohol,  or  by  burning  gas  in  a  Bunsen's 
burner.    If  a  platinum  wire  be  dipped  in  common  salt,  or  in 
any  sodium  compound,  and  held  in  a  colorless  flame,  the 
sodium  will  vaporize  and  emit  a  very  pure  yellow  light. 
Lithium  yields  a  pure  red.     Several  other  substances  yield 
characteristic  colored  flames:    thus,  strontium  gives  a  red 
color  ;  potassium,  purple ;  copper,  green. 

291.  The  spectroscope  is  an  instrument  used  for  analyz- 
ing flames.     Fig.    170.      The    substance   which    colors    the 
flame  is  placed   on   platinum  wires  in  a  Bunsen's  burner  at 
E,  and  vaporized.      The  light  which   it   emits   is   received 
through  a  narrow  slit  in  the  end  of  the  tube,  A,  where  it  is 
condensed    by  lenses  and   thrown    on    the  prism,  P.     The 
refracted  rays  fall  on  the  object-glass  of  a  small  telescope,  B, 
and  pass  through  it  to  the  eye.     The  tube,  C,  is  not  neces- 
sary, but  is  added  for  the  sake  of  convenience.     It  contains 
a  transparent  scale  which  is  divided  into  equal  parts.    When 


THE  SPECTROSCOPE. 


189 


a  candle  is  placed  in  front  of  C,  it  casts  a  bright  image  of 
the  scale  on  the  prism,  which  is  reflected  into  the  tube,  B, 


FIG.  170. 


so  that  the  observer  sees  at  once  the  refracted  rays  and  the 
lines  of  the  scale  to  which  they  correspond. 

Sodium  gives  a  bright  line,  identical  in  refrangibility  with 
the  dark  line,  D,  in  the  solar  spectrum.  Thallium  gives  a 
green  line  near  the  dark  line,  E.  The  light  emitted  .by 
these  substances  is  monochromatic ;  that  is,  of  only  one  color. 
Potassium  gives  a  red  line  near  A,  and  a  violet  ray  near  H. 
Strontium  gives  several  red  lines  between  B  and  D,  and  a 
blue  line  between  F  and  G.  The  light  emitted  by  these 
substances  is,  therefore,  not  homogeneous,  but  contains  two 
colors.  Any  substance  which  can  be  volatilized  will  furnish 
a  spectrum  of  a  few  bright  lines  which  have  a  constant 
degree  of  refrangibility.  This  is  also  true  of  incandescent 


190  ELEMENTS  OF  PHYSICS. 

gases :  hydrogen  yields  three  bright  lines,  which  are  iden- 
tical in  position  with  C,  F,  G.  If  several  substances  are 
mixed,  each  will  give  its  own  system  of  lines  as  if  it  were 
burned  separately.  This  property  has  been  turned  to 
account  in  chemistry  in  detecting  the  presence  of  sub- 
stances that  are  easily  volatilized.  For  these  bodies,  it  is  an 
exceedingly  sensitive  test.  It  is,  in  fact,  difficult  to  obtain 
a  flame  that  does  not  show  the  presence  of  sodium,  as 
T¥o¥W«nro  °f  a  grain  of  sodium  will  yield  its  yellow  line. 
Since  the  year  1860  four  new  metals  have  been  discovered 
by  the  aid  of  the  spectroscope.  Two  of  these,  caesium  and 
rubidium,  are  widely  distributed,  being  found  in  many  min- 
eral waters,  and  in  the  ashes  of  tobacco,  but  in  such  small 
quantities  that  the  usual  chemical  tests  failed  to  detect 
them. 

292.  If  light,  which  would  give  a  continuous  spectrum, 
is  passed  through  certain  almost   transparent   and  colorless 
solutions  and  then  examined,  dark  lines  are  found,  which 
are  owing  to  the  fact  that  the  solution  has  absorbed  some 
of  the  rays.     Thus,   solutions  of  didymium  give  two  dark 
lines,  one  in  the  yellow  and  the  other  in  the  green.     The 
gases   also  produce  absorption  bands;  the  vapors  of  iodine 
and   bromine    produce    remarkable    series   of   black    bands. 
Even  the  atmosphere  exerts  an  absorptive  power,  which  is 
especially    energetic    when    the    sun    is    near    the    horizon. 
Some  of  Fraunhofer's   lines   are,   undoubtedly,  due  to   the 
air,  but  the  larger  portion  must  have  another  cause. 

293.  If  two  sodium  flames  are  placed  before  the  spec- 
troscope,   so    that    one    must    pass    through    the    other,   no 
spectrum    is    produced.      In    other    words,    sodium    vapor 
absorbs    the    same    rays    that    it    emits.      So,    also,    if  the 
lime-light    which    gives    a   continuous    spectrum   is    passed 


SPECTR  UM  ANAL  YSIS.  191 

through  a  sodium  flame,  a  dark  line  is  found  in  the  place 
where  the  yellow  sodium  ray  should  be,  and  the  spectrum 
is  said  to  be  reversed.  These  phenomena  are  exhibited  by 
so  many  substances  that  we  may  group  the  effects  produced 
in  two  general  statements. 

(1)  Every  substance,  when  rendered  luminous,  gives  out  rays 
of  a  definite  degree  of  refrangibility. 

(2)  Every  substance  has  the  power  of  absorbing  the  same  kind 
of  rays  that  it  emits. 

294.  In  view  of  these  facts,  Kirchhoff  supposes  (1) 
that  the  nucleus  of  the  sun  emits  a  continuous  spectrum, 
containing  rays  of  all  degrees  of  refrangibility;  (2)  that  the 
luminous  atmosphere  of  the  sun  contains  vapors  of  various 
elements,  each  of  which  would,  by  itself,  give  its  system  of 
bright  lines  ;  (3)  that  when  the  light  from  the  nucleus  is 
transmitted  through  this  luminous  atmosphere,  the  bright 
lines  that  would  have  been  produced  by  the  atmosphere  are 
reversed ;  and  (4)  that  Fraunhofer's  lines  are  these  reversed 
lines. 

Since  the  bright  lines  of  the  elements  coincide  with  very 
many  of  Fraunhofer's  lines,  it  is  fair  to  suppose  that  these 
elements  exist  in  the  sun.  Iron  gives  four  hundred  bright 
lines  which  coincide  with  Fraunhofer's  lines.  Eighteen  dif- 
ferent metals  give  similar  coincidences.  Hence,  we  are  led 
to  suppose  that  the  sun  contains  iron,  manganese,  nickel, 
calcium,  copper,  sodium,  hydrogen,  and  some  other  ele- 
ments. Hitherto  no  evidence  has  been  given  of  the 
presence  of  gold,  silver,  mercury,  and  many  other  elements. 

The  fixed  stars  also  show  similar  coincidences ;  thus  Sirius 
and  Aldebaran  are  thought  to  contain  sodium,  magnesium, 
and  hydrogen.  The  comets  and  nebulae  give  spectra  with 
bright  lines,  which  seem  to  show  that  these  bodies  are 
incandescent  gases. 


192  ELEMENTS  OF  PHYSICS. 

295.  When  a  sunbeam  falls  on  a  film  of  oil  floating  on 
water,  or  on   a  soap-bubble,  we  notice  a  very  brilliant  dis- 
play of  colors.     The  light  is  reflected  to  our  eyes  both  from 
the  outer  and  inner  surface  of  the  film,  and  produces  the 
phenomena  of  interference  and  combination.     This  is  a  con- 
firmation  of  the   wave   theory  of  light.     We   may   obtain 
similar  phenomena  in  various  ways.     One  of  the  simplest 
methods  is  the  following :  Press  together  a  convex  lens,  A  B, 
of  long  radius  of  curvature,  upon 

a  plate  of  plane  glass,  D  E.     If  a 
beam  of  monochromatic  light  falls 

^*     J?  £       fr 

perpendicularly    on    the    lens,    a  F*G.  171. 

portion  of  it  will  be  reflected  from  the  convex  surface, 
ACB,  and  another  portion  from  the  plane  surface,  D  E. 
These  two  systems  of  waves  will  intersect  in 
crests  and  hollows  according  as  their  paths 
differ  by  an  even  number  of  semi-undulations, 
or  by  an  odd  number.  At  a  certain  distance 
FIG.  172.  from  0,  as  at  F,  the  two  waves  will  meet  in 
opposite  phases  and  destroy  each  other,  and,  hence  there 
will  be  a  black  ring  at  F.  At  a  greater  distance,  as  at  G, 
the  waves  will  meet  in  the  same  phase  and  increase  the 
amplitude  of  vibrations,  and  there  will  be  a  bright  ring  of 
the  same  color  as  the  light.  Other  points  will  be  found 
beyond  G,  in  which  the  waves  will  meet  in  opposite  or  in  sim- 
ilar phases,  and,  consequently,  a  series  of  black  and  colored 
rings  will  be  found  about  the  center,  C. 

If  the  solar  light  be  employed,  each  ring  contains  all  the 
colors  of  the  spectrum,  because  the  colors  have  different 
refrangibilities,  and  the  rings  are  not  exactly  superimposed. 

296.  These  rings  are  known  as  Newton's  rings.     Now, 
as  we   can   calculate  exactly  the  distance  between   the  two 
surfaces,  we  have  a  means  of  determining  the  wave  length 


COLOR  OF  LIGHT. 


193 


due  to  various  colors.     The  following  table  has  been  con- 
structed in  accordance  with  these  data  : 


Colors. 

Lengths  of  waves 
in  parts 
of  an  inch. 

Number 
of  waves  in  an 
inch. 

Number 
of  waves  in  a 
second. 

Extreme  red  .  .  . 
Red  

.0000266 
.0000256 

37640 
39180 

442000000000000 
458000000000000 

.0000240 

41610 

489000000000000 

Yellow  

.0000227 

44000 

517000000000000 

.0000211 

47460 

558000000000000 

Blue  

.0000196 

51110 

599000000000000 

.0000185 

54070 

634000000000000 

Violet  

.0000174 

57490 

675000000000000 

Extreme  violet  . 

.0000167 

59750 

702000000000000 

297.  The  color  of  light  is  determined  by  the  frequency 
of  its  vibration,  or  by  the  length  of  its  wave.     Light  and 
sound  are  somewhat  similar.     We  found  that  the  low  tones 
have  a  slow  rate  of  vibration  and  a  great  wave  length.     So 
the  luminous  rays  that  are  the  least  refracted  are  longer  and 
slower  than  those  that  are  more  refracted.     But  the  student 
will  not  fail  to  notice  how  very  small  and  how  very  rapid 
are  light  waves  when  compared  with  sound  waves. 

298.  It  is  usual  to  classify  the  properties  of  the  spec- 
trum in  three  groups :    Luminous,  Heating,  and  Chemical. 
Every  ray  possesses,  it  is  probable,  all  of  these  properties, 
but  not  in  equal  intensity.     Thus  the  maximum  chemical 
effect  is  found  in  the  rays  of  high  refrangibility ;    the  maxi- 
mum heating  effect  in  the  rays  of  low  refrangibility;    the 
maximum  luminous  effect  in  the  rays  of  nearly  mean  refran- 
gibility, viz. :    the  yellow.     The  curves  in    Fig.  167,   show 
the  relative  intensity  of  each  property  in  a  spectrum   pro- 
duced by  flint-glass.     It  will  be  noticed   that  the  spectrum 

PlIYS.   17. 


194  ELEMENTS  OF  PHYSICS. 

is  drawn  as  if  extending  beyond  the  colored  rays ;  that  is 
to  say,  there  are  heat  rays  that  the  eye  can  not  perceive 
because  their  rate  of  vibration  is  too  slow,  and  there  are 
chemical  rays  which  it  can  not  perceive  because  their  rate 
of  vibration  is  too  great.  These  invisible  rays  do  not  differ 
in  kind  from  the  visible  rays. 

Some  persons  are  color-blind,  and  can  not  distinguish 
colors  at  all,  although  in  every  other  respect  their  sight  is 
perfect.  The  most  common  defect  of  this  sort  is  an  in- 
ability to  distinguish  red  colors.  A  person  "red-blind" 
believes  that  ripe  cherries  are  of  the  same  color  as  the 
leaves  which  hang  near  them. 

299.  The  natural  color  of  a  body  is  due  to  the  power 
it  has  of  extinguishing  certain  vibrations,  and  of  reflecting 
or  transmitting  others.  A  red  cloth  reflects  the  red  rays  and 
absorbs  the  rest ;  red  glass  transmits  only  the  red  rays.  A 
body  that  reflects  all  the  rays  of  the  solar  spectrum  is 
white  ;  a  body  that  reflects  but  very  little  light  is  black. 

A  curious  experiment  illustrates  that  the  color  of  a  body 
is  not  inherent.  Darken  a  room,  and  then  set  on  fire  a  cup 
of  alcohol  which  has  been  saturated  with  common  salt: 
every  object  will  be  illuminated  by  the  yellow  light  of 
sodium,  and  appear  of  a  yellow  color.  As  this  light  falls 
on  the  faces  of  those  near  the  cup,  it  gives  them  a  ghastly 
appearance,  which  is  quite  wonderful  to  those  who  see  the 
effect  for  the  first  time. 

RECAPITULATION. 

When  solar  light  is  examined  with  a  prism,  it  is  found  to  consist 
of  seven  primary  colors,  which  are  interrupted  by  dark  lines. 

Other  luminous  bodies  yield  spectra  which  resemble  the  solar 
spectrum  in  many  particulars. 

All  spectra  have  luminous,  thermal,  and  chemical  properties,  but 
not  in  equal  intensity. 


COLORS.  195 

The  spectrum   analysis  depends  on  the  fact  that  every  luminous 
body  emits  rays  of  definite  refrangibility. 

The  dark  lines  are  explained  by  the  fact  that  every  luminous  body 
is  capable  of  absorbing  the  rays  which  it  emits. 

Luminous  vibrations  may  be   made   to   combine  and  interfere  by 
reflection  and  refraction. 

Colors  are  dependent  on  the  frequency  of  the  luminous  vibrations. 

PEOBLEMS. 

1.  It  is  calculated  that  the  light  from  the  polar  star  requires  3£ 
years  to  reach  the  earth ;   what  is  its  distance  ? 

2.  What  are   the   relative  intensities  of  two  lights  that  cast  equal 
shadows  at  distances  from  an  opaque  rod   respectively  6  inches  and 
6  feet? 

3.  A  wax  candle  is  fixed  at  10  inches  from  the  opaque  rod ;  what 
must  be  the  distance  of  a  gas-light  from  the  same   rod  to   cast  an 
equal  shadow  when  the  gas  burns  with  "12  candle  power?" 

4.  What  will   be  the  index  of  refraction  when   light  passes  from 
crown-glass    into  bisulphide   of   carbon?     When    it    passes  'in    the 
other  direction? 

5.  What  will  be  the  relative  lengths  of  two  solar  spectra  produced 
under  the  same  circumstances  by  prisms  of  quartz  and  of  bisulphide 
of  carbon? 

6.  With  red  taken  as  unity,  find  the  ratio  between   the  relative 
number  of  vibrations    in    the    colors   of   the   spectrum,  and  compare 
with  the  relative  number  of  sonorus  waves  in  an  octave.     Will  the 
comparison  warrant  any  analogy  between  vibrations  of  light  and  of 
sound? 


CHAPTER  XV. 

THE  PHENOMENA  OF  HEAT,  OR  PYRONOMICS. 

300.  The  phenomena  of  heat  are  so  generally  manifest 
that  we  have  had  frequent  occasion  to  refer  to  them,  and 
have  explained  the  methods  by  which  heat  may  be  meas- 
ured. It  may  be  noticed  that  our  sensations  of  warmth  and 
cold  are  only  relative,  and  are  sometimes  utterly  untrust- 
worthy as  a  means  of  measuring  heat.  If  we  place  the 
right  hand  in  iced  water  and  the  left  in  hot,  and  then 
transfer  both  to  ordinary  cistern  water,  the  left  hand  will 
pronounce  the  cistern  water  cold  and  the  right  hand  pro- 
nounce it  warm.  So,  also,  if  we  pass  from  the  outer  air  of 
a  winter's  day  into  a  heated  room,  our  sensations  may  lead 
us  to  declare  it  overheated,  even  while  the  occupants  of  the 
room  are  somewhat  chilly. 

We  have  also  noticed  that  one  effect  of  heat  is  to  render 
bodies  incandescent,  and  that  the  solar  rays  have  their  maxi- 
mum heating  effect  near  the  red  rays.  These  phenomena, 
as  well  as  others  that  we  shall  have  occasion  to  study,  so 
connect  heat  with  light  that  we  are  almost  justified  in  assum- 
ing that  their  phenomena  are  due  to  the  same  force.  Both  are 
certainly  forms  of  energy  by  which  molecules  of  matter  are 
thrown  into  vibrations  and  give  rise  to  waves  of  crests  and 
hollows.  They  differ  in  the  fact,  that  the  eye  recognizes  as 
light  only  those  waves  which  have  certain  limits  of  rapidity 
of  motion,  and  which  are,  at  best,  very  small,  while  waves 
of  heat  can  be  recognized  that  are,  in  comparison,  large  and 
of  slow  rate  of  motion;  although  it  is  not  meant  to  be 
(196) 


EFFECT  OF  HEAT. 


197 


stated  by  this  that  heat  waves  may  not  also  accompany,  or 
be  identical  with,  the  most  refrangible  luminous  waves. 

Besides  these  phenomena,  heat  produces  certain  effects 
within  the  bodies  upon  which  it  acts,  which  we  shall  now 
proceed  to  consider. 

301.  The  first  effect  of  heat  on  any  body,  solid,  liquid, 
or  aeriform,  that  is  not  destroyed  by  it,  is  to  expand  it. 

The  expansion  of  gases  may  be  shown  by  the  air- ther- 
mometer. Fig.  173.  This  consists  of  a  bulb  of  glass  with 
a  long  stem,  which  dips  into  a  colored  fluid.  ^. 

If  the  bulb  be  warmed  by  the  hand,  the 
air  inclosed  will  so  expand  that  a  portion 
will  be  expelled  and  rise  in  bubbles  through 
the  fluid.  On  cooling,  that  portion  of  the 
air  which  remains  will  contract  to  its  former 
volume,  and  the  fluid  will  rise  to  take  the 
place  of  the  air  expelled. 

On  repeating  this  experiment  with  other 
gases,  it  will  be  found  that  att  aeriform 
bodies  expand  equally  and  regularly  for  equal 
successive  incitements  of  temperature.  The  ex- 
pansion is  T|T  for  each  degree  F.,  or 
for  each  degree  C. 

The  expansion  of  liquids  may  be  shown  by  a  flask 
having  a  long  narrow  tube  fitted  to  its  neck  by  a  cork. 
Fig.  174.     If  the  flask  be  filled  with  alcohol  and 
plunged    in    boiling   water,   the    expansion  of  the 
alcohol  will  be  shown  by  its  rise  in  the  tube.     Coal 
oil   expands   more    than    alcohol,    but   most    other 
liquids   less,   showing    that    different    liquids   expand 
unequally  for  the  same  increments  of  temperature. 
FIG.  174.    ]y[ore   accurate  experiments  show  that  each   liquid 
also  expands  irregularly.     On   being  raised  from  32°  F.  to 


FIG.  173. 


198  ELEMENTS  OF  PHYSICS. 

212°  F.  alcohol  expands  ^  of  its  volume,  water  about  ^T, 
and  mercury  -%-%. 

The  expansion  of  solids  may  be  illustrated  by  the  ap- 
paratus given  in  Fig.  5.  *  These  experiments  show  an 
increase  in  volume  which  is  termed  cubical  expansion.  In 
solids  the  expansion  is  sometimes  measured  in  one  direction 
only,  and  is  then  termed  linear  expansion. 

Fig.  175  represents  the  pyrometer,  an  instrument  which 
shows  the  linear  expansion  of  solids,  and  which  is  sometimes 


FIG.  175. 

used  to  measure  very  high  temperatures.  A  metallic  rod, 
A,  fixed  at  one  end,  B,  presses  at  the  other  end  the  short 
arm  of  the  index,  K.  When  the  rod  is  heated  it  expands 
and  drives  the  index  along  the  scale. 

302.  Different  solids  expand  unequally  for  equal  in- 
crements of  temperature.  If  two  thin  bars  of  iron  and 
brass  are  riveted  together  at  different  points  along  their 
whole  length,  and  boiling  water  is  poured  on  them,  it  will 


FIG.  176.  FIG.  177. 

bend  so  that  the  brass  will  be  on  the  convex  side  of  the 
curve.  If  it  is  then  plunged  in  cold  water,  it  will  curve  in 
the  opposite  direction.  The  reason  of  this  is,  that  the  brass 
expands  and  contracts  more  than  the  iron,  and  the  bar 
curves,  so  that  the  longest  bar  shall  be  on  the  convex  side. 


EXPANSION.  '         199 


Tabk  of  Expansion  from  32°  F.  to  212°  F. 

Linear.         Cubical.  Linear.      Cubical. 

Flint-glass    .    ^s      ^  Brass    .    .    .    .    -gfa 

Platinum  .    .    y^       ^  Silver  ....    -5^4 


Steel    ....      ^       3^  Tin   .....    ?)-L-       ^ 

Iron       ....         -^          ^k  ZinC       •     •     •     •     1*7         TT3 


The  fractions  in  the  above  table  of  linear  expansion  show 
what  proportion  of  its  length  a  body  will  increase  in  being 
raised  from  32°  F.  to  212°  F.  It  will  be  noticed  that  the 
cubical  expansion  is  expressed  by  a  fraction  three  times  as 
large.  With  very  few  exceptions,  all  bodies  contract  on 
cooling  to  their  original  dimensions. 

303.  When  water  is  heated  from  32°  F.  to  212°  F.  it 
expands  .0466  of  its  volume  ;  it  is  compressed  by  a  pressure 
of  one  atmosphere  .000044  of  its  volume.  Therefore,  it  would 
require  a  pressure  of  over  1000  atmospheres  to  restore  boil- 
ing water  to  its  bulk  when  at  the  freezing  point,  or  to  pre- 
vent its  expansion  on  being  heated  180°.  We  see  from  this 
that  the  amount  of  force  exerted  in  expansion  or  contrac- 
tion by  heat  is  enormous.  The  expansive  force  of  water  for 
each  degree  F.  is  nearly  y%0/  =  6  atmospheres,  or  90  pounds 
per  square  inch. 

A  bar  of  wrought  iron  expands  for  each  degree  F.  with  a 
force  of  nearly  two  hundred  pounds  per  square  inch.  Hence, 
it  is  often  necessary  to  take  into  account  the  changes  in 
length  which  are  produced  by  variations  in  temperature. 
Iron  beams  built  into  masonry  should  be  left  free  at  one 
end. 

We  have  an  application  of  the  same  principle  in  the 
method  by  which  tires  are  secured  on  wheels.  The  tire, 
made  a  little  smaller  than  the  wheel,  is  heated  red-hot,  and, 


200  ELEMENTS  OF  PHYSICS. 

while  expanded,  placed  in  position.  On  cooling,  it  not  only 
secures  itself  on  the  rim,  but  holds  all  the  other  parts  of 
the  wheel  in  position. 

Brittle  substances,  as  glass  or  cast-iron,  often  crack  when 
heated  suddenly ;  because  the  outside  is  heated  sooner  than 
the  inside,  and  thereby  causes  an  unequal  expansion.  The 
thicker  the  plate,  the  greater  the  liability  to  fracture.  A 
sudden  cooling  by  producing  an  unequal  contraction,  has  the 
same  tendency  to  fracture. 

304.  Water  presents  an  exception  to  the  general  law  of 
expansion  and  contraction  by  heat.     If  a  flask  with  a  long 
and  very  slender  neck,  Fig.  174,  be  filled  with  boiling  water 
and  allowed  to  cool,  the  water  will  contract  until  it  reaches 
the  temperature  of  39°. 2   F.     It  then  begins  to  expand, 
and  continues  to  do  so  until  it  freezes.     At  32°  F.  it  occu- 
pies the  same  space  that  it  did  at  48°  F.     The  maximum 
density  of  water  is,  therefore,  attained  at  39°'. 2  F.,  and  above 
or  below  this  temperature  it  expands. 

This  fact  is  of  infinite  importance  in  nature.  In  winter, 
the  lakes  and  rivers  cool  until  they  attain  their  maximum 
density  throughout.  If  the  cooling  proceeds  further,  expan- 
sion begins  at  the  surface,  and  the  lighter,  though  colder, 
particles  float  on  the  warmer  particles  below.  Hence,  the 
freezing  takes  place  only  at  the  surface. 

At  the  moment  of  freezing,  water,  in  becoming  solid  ice, 
undergoes  a  sudden  increase  of  about  ten  per  cent  in 
volume.  The  ice,  once  formed,  covers  the  water  like  a 
blanket,  and  renders  the  freezing  process  very  slow.  If  the 
ice  had  a  greater  specific  gravity  than  water,  it  would  sink 
to  the  bottom,  and  in  time  our  lakes  would  become  solid. 

305.  The  second  effect  of  heat  on  a  solid  is  to  melt  it. 
Some  solids,  as  paper,  wood,  wool,  do  not  melt,  but  are  de- 
composed.     The   temperature   at  which   any  solid   melts  is 


FUSION.  201 

invariable  for  the  same  substance,  if  the  pressure  is  the 
same.     This  temperature  is  called  the  melting  point. 

Table  of  Melting  Points,  in  Degrees  Fcdirenlieit. 

Mercury"   ....      -37.9  Bismuth     ....  512. 

Bromine     ....     -f-    9.5  Lead 620. 

Ice 32.  Zinc 680. 

Phosphorus     ....  111.5  Silver        ....  1832. 

Potassium       ....  136.  Gold     .....  2282. 

Tin        451.  Wrought  Iron    .     .  2912. 

Certain  bodies,  as  iron,  platinum,  glass,  and  wax,  soften 
before  they  fuse  and  become  plastic.  It  is  in  this  plastic 
state  that  glass  is  worked  and  iron  or  platinum  forged. 
The  melting  point  of  alloys  is  often  lower  than  that  of 
either  of  its  components.  Rose's  metal,  which  consists  of 
four  parts  of  bismuth,  one  of  lead,  and  one  of  tin,  fuses  at 
201°  F. 

306.  If  a  liquid  is  cooled  sufficiently  it  generally 
solidifies  at  the  melting  point,  but  the  freezing  point  may 
be  lowered  by  various  means. 

If  water  is  boiled  to  expel  the  air  and  then  allowed  to 
cool  very  slowly  and  without  agitation,  it  sometimes  reaches 
10°  F.  before  it  freezes.  When  in  this  condition,  any  dis- 
turbance, as  a  jolt  or  the  addition  of  a  bit  of  ice,  will  cause 
immediate  congelation  throughout  the  entire  mass.  The 
temperature  will  rise  to  32°  F.  In  fine  capillary  tubes, 
water  has  been  lowered  to  —  4°  F.  without  solidifying.  This 
probably  explains  why  sap  is  not  frozen  in  plants. 

The  presence  of  salts  in  solution  lowers  the  freezing  point 
of  water.  Saturated  brine  freezes  at  —  4°  F.  Sea-water 
freezes  at  27°. 4  F.  In  such  cases,  nearly  pure  ice  is  formed. 
The  water  appears  to  crystallize  out,  leaving  the  salt  behind. 
Weak  alcoholic  mixtures,  like  wine  and  cider,  may  be  con- 


'202  ELEMENTS  OF  PHYSICS. 

centrated  by  exposing  them  to  cold  and  removing  the  layers 
of  ice  as  they  form. 

307.  Water  expands  with  enormous  force  at  the  mo- 
ment of  freezing.      Bomb-shells  an  inch  thick,  filled  with 
water,  have  been  burst  by  the  freezing  of  the  water.     On  a 
smaller  scale,  the  fact   is   familiar   to   northern   housekeep- 
ers  in   the  breaking  of  utensils  in   which  water  has  been 
allowed  to  freeze.     Cast-iron,  bismuth,  antimony,  and  type- 
metal   also  expand  on  solidifying.     These  substances  give 
sharp  casts,   because,  when  the    metal  gets,  the  expansion 
forces  it  into   the  minute  lines  of  the  mold.      Most  sub- 
stances contract  on  solidifying.     Coins  of  copper,  silver,  and 
gold  are  not  cast,  but  stamped. 

308.  The  third  effect  of  heat  is  vaporization.     Some 
solids,  as   iodine,  arsenic,   and    camphor,  vaporize    without 
becoming  liquids  ;    but,  generally,  vapors  are  formed  from 
liquids,  as  liquids  are  from  solids.     If  the  vaporization  takes 
place  quietly,  it  is  termed  evaporation;  but,  if  the  liquid  is 
agitated  by  the  formation  of  bubbles  of  its  own  vapor,  the 
process  is  termed  boiling. 

309.  The  evaporation  of  water  is  going  on  constantly 
in  nature,  and  is  one  of  the  means  by  which  the  earth  is 
rendered  fit  for  the  maintenance  of  life.     The  principal  cir- 
cumstances which  influence  the  evaporation  of  water  are  the 
following : 

(1)  The  temperature.  Evaporation  may  go  on  at  very  low 
temperatures.  Snow  and  ice  disappear  from  the  ground 
even  when  there  has  been  no  thawing.  Clothes  are  dried 
on  a  winter's  day  when  the  thermometer  shows  a  tempera- 
ture below  freezing.  Increase  of  temperature  favors  evap- 
oration. In  summer,  the  roads  are  soon  dry  after  a  shower, 
"because  the  evaporation  is  rapid. 


EVAPORATION.  203 

(2)  Tlie  amount  of  surface  exposed;    because   evaporation 
proceeds  only  from  the  surface. 

(3)  Tlie  condition  of  the  air.     The  air  can   hold   only  a 
limited  amount  of  aqueous  vapor.     At  32°  F.   one  cubic 
foot  of  air  can  hold  only  2.37  grains  of  aqueous  vapor,  which 
is  ^-s-Q  part  of  its  weight.     For  every  increase  of  20°  F.  the 
capacity  of  air  for  moisture  is  nearly  doubled ;    at  52°  F.  it 
can  absorb  T^-§-  part  of  its  weight ;  at  72°  F.  about  •£§  part, 
and  so  on.     When  air  contains  as  much  moisture  as  it  can 
hold,  it  is  said  to  be  saturated,  and  evaporation  must  cease. 
Therefore,  evaporation  is  most  rapid  in  dry  air. 

Now,  if  the  air  above  a  liquid  is  not  changed,  it  becomes 
saturated.  Hence,  evaporation  is  more  rapid  in  a  breeze 
than  in  still  air.  For  this  reason  a  warm,  sultry  day  is  less 
favorable  to  evaporation  than  a  cold  day  with  a  brisk  wind. 

310.  Suppose  air  at  72°  F.  to  be  saturated  with  moist- 
ure, and  then  to  cool  gradually.  As  the  temperature  low- 
ers, its  capacity  for  moisture  decreases,  and  a  portion  of  the 
moisture  present  will  be  deposited  as  dew.  If  the  tempera- 
ture falls  to  52°  F.  half  of  the  original  quantity  will  have 
been  deposited.  Now,  suppose  the  air  at  72°  F.  to  have 
been  nearly  but  not  quite  saturated ;  as  the  temperature  is 
lowered,  a  point  will  be  reached  at  which  the  air  is  satu- 
rated, and  then  a  temperature  at  which  the  dew  will  begin 
to  form.  This  last  temperature  is  called  the  dew-point. 

The  dew-point  may  be  determined  with  sufficient  accuracy 
for  ordinary  purposes  by  placing  ice  in  a  tin  cup  containing 
water,  and  noting,  by  a  thermometer,  the  temperature  of 
the  water  when  the  dew  begins  to  form  on  the  outside  of  the 
vessel.  The  "  sweating"  of  pitchers  is  an  indication  of  rain, 
because  it  shows  that  the  air  is  nearly  saturated  with  moist- 
ure, which  will  fall  if  the  temperature  of  the  air  is  lowered 
below  the  dew-point. 


204  ELEMENTS  OF  PHYSICS. 

Our  comfort  depends  largely  on  the  amount  of  moisture 
present  in  the  atmosphere.  If  the  air  is  saturated,  the  per- 
spiration is  not  carried  off  from  our  bodies ;  if  it  is,  at  the 
same  time,  warm,  we  perspire  more,  and  the  air  is  said  to 
be  sultry.  If  the  air  is  too  dry,  the  moisture  is  carried  off 
too  rapidly  from  our  lips  and  eyelids,  and  they  become  dry. 

311.  The  temperature  at  which  liquids  boil  is  con- 
stant for  the  same  substance,  under  like  conditions.  Sev- 
eral conditions  influence  the  boiling  point: 

1.  The  nature  of  the  liquid.     The  boiling  point  of  several 
liquids  under  the  pressure  of  one  atmosphere  is  given  below. 

Table  of  Soiling  Points. 

Nitrous  oxide      .     — 157°  F.  Bromine  .  .  145°.4  F. 

Carbonic  acid      .     —108.4  Alcohol  .  .  .  173.1 

Sulphurous  acid       -f    17.6  Water  .  .  .  212. 

Ether 94.8  Mercury  .  .  .  662. 

2.  The  adhesion  of  the  liquid  to  the  vessel  that  contains  it. 
Water  sometimes  boils  in  a  glass  vessel  at  214°  F. ;    espe- 
cially  is  this  apt   to  be   the   case   if  the  water  has  been 
deprived  of  air  by  previous  boiling. 

3.  Salts  in  solution  increase  the  boiling  point.      A  satu- 
rated solution  of  common  salt  boils  at  227°  F.;  of  calcium 
chloride  at  355°  F.      Substances  mechanically  suspended, 
like  sawdust,  do  not  influence  the  boiling  point.      The  steam 
which  forms  in  the  last  two  conditions  assumes  almost  imme- 
diately the  temperature  of  212°  F. 

4.  Variations  of  pressure.     A  liquid  boils  when  the  tension 
of  its  vapor  is  equal  to  the  pressure  which  it  supports.     If 
a  cup  containing 'ether  be  placed  under  the  receiver  of  an 
air-pump,  the  ether  will  boil  when  the  receiver  is  partially 
exhausted.      So,  also,  tepid  water  may  easily  be  made  to 
boil  in  an  exhausted  receiver. 


BOILING  POINT. 


205 


FIG.  178. 


The  culinary  paradox  illustrates  the  same  principle.  A 
flask  containing  boiling  water  is  tightly  corked  while  the 
steam  is  escaping,  and  in- 
verted. If,  now,  cold  water 
be  poured  on  the  bottom  of 
the  flask,  the  boiling  will  be 
renewed.  The  reason  of  this 
is,  the  cold  water  condenses 
the  steam  above  the  water, 
produces  a  partial  vacuum, 
and  thus  diminishes  the  pres- 
sure on  the  liquid. 

The  sirup  of  sugar  and  of 
vegetable  extracts  are  concen- 
trated in  closed  vessels,  called 
vacuum  pans.  A  powerful  air-pump  constantly  removes  the 
pressure  from  the  pan,  and,  consequently,  the  evaporation 
proceeds  at  a  temperature  so  low  that  it  secures  the  sirup  or 
the  extract  from  injury  by  heat. 

312.  A  variation  of  an  inch  in  the  barometric  column 
makes  a  difference  of  about  2°  F.  in  the  boiling  point  of 
water.  The  atmospheric  pressure  is  lowered  on  ascending 
mountains;  hence,  water  boils  at  lower  temperatures  on 
mountains  than  at  the  sea  level.  A  difference  of  600  feet  of 
ascent  makes  a  variation  of  about  1°  F.  in  the  boiling  point. 

Under  increased  pressures  the  boiling  point  is  raised.  If 
\vater  be  placed  in  a  small  boiler,  Fig.  179,  furnished  with 
a  thermometer,  a  manometer,  and  a  stop-cock,  and  boiled,  it 
will  be  found  that  so  long  as  the  stop-cock  is  open  the  tem- 
perature of  boiling  will  remain  steadily  at  212°  F.  On 
closing  the  cock  the  boiling  point  will  rise,  because  the 
steam  which  continues  to  form  increases  in  elastic  force,  and 
produces  pressure  on  the  water.  When  the  manometer 


206 


ELEMENTS  OF  PHYSICS. 


shows   a  pressure  of  thirty  inches  of  mercury,   the  boiling 
point  will  equal  249°.  5  F.    This  is  the  boiling 
point  due  to  two  atmospheres :    one  shown  by 
the  manometer ;    the   other,  the  atmospheric 
pressure  present  before  closing  the  cock. 

If  steam  is  formed  in  a  boiler  and  then 
conducted  through  red-hot  tubes,  it  follows 
the  general  law  for  expansion  of  gases,  and 
is  then  called  superheated  steam.  Such  steam 
is  applied  to  the  rendering  of  fats. 

313.   Every  one  must  have  noticed  that 
when  drops  of  water  are  thrown  on  a  heated 
stove   they  roll    about,   becoming    gradually 
smaller,  and    finally   disappear   in  a  sort  of 
explosion.     The  explanation  of  this  phenom- 
enon is,  that  as  soon  as  the  drop  reaches  the          FIG.  179. 
surface  a  portion  of  it  is  converted  into  vapor,  which  sup- 
ports the  liquid  and  prevents  it  from  touching  the  heated 
metal.     The  drop  assumes  what  is  called  the  spheroidal  state, 

and  evaporates  at  a  temper- 
ature lower  than  its  boiling 
point.  If  a  copper  flask  be 
intensely  heated,  and  a  small 
quantity  of  water  poured 
in,  the  water  will  assume 
the  spheroidal  condition,  and, 
for  a  time,  all  will  appear 
quiet.  Fig.  180.  Now  cork 
the  flask  and  remove  the 
source  of  heat.  When  the 
flask  has  sufficiently  cooled, 
the  water  will  come  in  con- 
tact with  its  surface,  and  so  much  steam  will  be  formed 


FIG.  180. 


LIQUEFACTION  OF  VAPORS. 


207 


suddenly  that  the  cork  will  be  ejected  with  violence.  It  is 
probable  that  boiler  explosions  are  sometimes  caused  in  a 
similar  manner. 

There  are  some  curious  phenomena  which  are  due  to  the 
spheroidal  state.  Thus,  if  sulphurous  acid  is  thrown  into  a 
capsule  heated  white  hot,  it  assumes  a  spheroidal  state,  and 
remains  at  a  temperature  of  13°  F.  Water  thrown  into  it 
will  instantly  freeze.  So,  also,  a  hand  moistened  with  water 
may  be  drawn  without  injury  through  molten  iron  as  it  runs 
from  the  furnace.  The  moisture  forms  a  non-conducting 
envelope  which  sufficiently  protects  the  hand  during  the 
short  period  of  its  immersion. 

314.  A  saturated  vapor  condenses  into  a  liquid  at  its 
boiling  point.  The  process  of  distillation  illustrates  this 


m^. 

•     | 

f^ 

si 

II 

^.-^ 

~j~ 

'___ 

1 

FIG.  181. 


fact.  It  is  used  to  separate  volatile  liquids  from  mix- 
tures. Fig.  181  represents  a  common  still :  the  boiler,  a, 
contains  the  liquid  to  be  evaporated;  the  spiral  tube,  del, 


208  ELEMENTS  OF  PHYSICS. 

which  is  called  a  worm,  receives  the  vapors  from  the  boiler. 
The  worm  is  kept  cool  by  being  surrounded  with  cold  water, 
and  the  vapors  condense  within  it  and  run  into  a  suitable 
receptacle. 

KECAPITULATION. 

The  effects  of  heat  are : 
1    The  expansion  and  contraction  of  bodies. 

2.  The  melting  and  solidifying  of  solids. 

3.  The  vaporization  and  condensation  of  liquids. 

4.  The  incandescence  and  cooling  of  solids. 


SPECIFIC  AND  LATENT  HEAT. 

315.  Let  us  now  consider  some  facts  relative  to  the 
amount  of  heat  which  is  required  to  produce  changes  of  tem- 
perature in  known  weights  of  different  substances.  We  as- 
sume as  a  relative  measure  of  the  quantity  of  heat  that  may 
be  gained  or  lost  by  a  body  the  thermal  unit,  which  is  the 
amount  of  heat  required  to  raise  one  pound  of  water  from 
32°  F.  to  33°  F. 

Suppose,  now,  that  we  have  a  uniform  source  of  heat,  as 
an  alcohol  lamp  that  consumes  a  pint  of  alcohol  an  hour, 
and  suppose  that  in  our  experiments  no  heat  is  wasted  in 
heating  the  apparatus,  or  the  surrounding  objects.  If  we  em- 
ploy this  heat  in  warming  different  substances,  we  should 
find  two  sets  of  phenomena:  those  of  specific,  and  of  latent 
heat. 

SPECIFIC  HEAT.  If  one  pound  of  water  were  raised  from 
32°  F.  to  33°  F.  in  a  given  time,  the  same  amount  of  heat 
would  be  competent  to  raise  five  pounds  of  sulphur  or 


SPECIFIC  HEAT.  209 

thirty  pounds  of  mercury  from  32°  to  33°  F.,  or  would  raise 
one  pound  of  sulphur  five  degrees  F.  and  one  pound  of  mer- 
cury thirty  degrees  F.  The  heat  required  to  raise  one  pound 
of  any  substance  through  1°  F.,  compared  with  the  thermal 
unit,  is  called  the  Specific  Heat  of  the  substance. 

316.  We  may  determine  the  specific  heat  of  bodies  by 
reversing  this  experiment.     Suppose  equal  weights  of  differ- 
ent bodies  be  heated  to  the  same  temperature  in  a  bath  of 
boiling  water  or  oil,  and  then  placed  in  cavities  in  a  cake  of 
ice.     In  comparison  with  water,  sulphur  will  melt  i,  iron  J, 
and  mercury  ^  as  much  ice.    These  fractions  express  the  spe- 
cific heats  of  these  substances,  because  the  heat  given  out  in 
cooling  is  precisely  equivalent  to  that  required  to  raise  the 
same  body  through  the  same  number  of  degrees. 

317.  The  specific  heat  of  aeriform  bodies  may  be  de- 
termined by  passing  a  heated  gas  through  the  worm  of  a 
distilling   apparatus,   and    noting    the   rise   in    temperature 
produced   in   the  water  when    a   given  weight   of  gas   has 
been  cooled  to  a  known  temperature. 

318.  The  specific  heat  of  a  substance  increases  slightly 
with    a    rise    in    the    temperature,  and   is    generally   much 
greater  in  the  liquid  state  than   in  either  the  solid  or  the 
aeriform  condition.     These  facts  are  shown  in  the  annexed 
tables. 

Tables  of  Specific  Heat. 

Between  Between 

32°  F.  and  212°  F.    32°  F.  and  572°  F. 

Mercury 0330  .0350 

Silver 0557  .0611 

Iron 1098  .1218 

Glass 1770  .1900 

PHYS.  18. 


210  ELEMENTS  OF  PHYSICS. 

Aeriform.  Liquid.  Solid. 

Water 4805  1.0000  .5050 

Bromine 0555  .1060  .0843 

Lead .0482  .0314 

Alcohol 4534  .5050 

Equal  volumes.       Equal  weights. 

Air 2375  .2375 

Oxygen 2405  .2175 

Hydrogen 2539  3.4090 

Turpentine 2.3776  .5061 

319.  With  the  exception  of  hydrogen,  water  possesses 
the  highest  specific  heat  known.  The  presence  of  large 
bodies  of  water  has,  for  this  reason,  a  marked  effect  on  the 
climate,  owing  to  the  large  amounts  of  heat  which  seas 
absorb  and  emit  in  accommodating  themselves  to  changes  in 
external  temperatures.  An  oceanic  climate  is,  therefore, 
more  equable  than  an  inland  climate  ;  its  summers  are  cooler 
and  its  winters  warmer. 

On  the  islands  of  Lake  Erie,  water  does  not  freeze  until 
the  water  of  the  lake  has  cooled  to  40°  F.,  thus  prolonging 
the  season  sufficiently  to  ripen  grapes.  A  daily  effect 
is  witnessed  in  tropical  islands  in  the  land  and  sea-breezes. 
While  the  sun  shines,  the  land  becomes  warmer  than  the 
ocean,  and,  by  consequence,  the  air  above  the  land  becomes 
rarefied  by  the  heat,  and  is  displaced  by  the  cold  air  which 
presses  in  from  the  ocean,  and  a  sea-breeze  is  produced ;  in  the 
night,  the  land  is  sooner  cooled,  the  air  above  it  becomes 
more  dense  and  flows  out  to  the  ocean  in  a  land-breeze. 

LATENT  HEAT.  These  facts  show  that  different  bodies 
require  different  quantities  of  heat  in  order  to  increase  their 
temperature.  Suppose,  now,  that  we  employ  heat  sufficient 


LATENT  HEAT.  211 

to  melt  them  or  to  vaporize  them.  If  a  thermometer  be 
placed  in  a  basin  filled  with  melting  ice,  it  will  remain  at 
32°  F.  until  the  whole  is  melted.  The  temperature  will 
then  rise  to  212°  F.,  and  then  again  become  constant  until 
all  the  water  is  changed  to  steam.  So,  generally,  a  body  in 
the  ad  of  changing  its  state  in  melting  or  in  vaporizing  maintains  a 
constant  temperature.  Now,  it  is  manifest  that  a  considerable 
amount  of  heat  is  required  to  effect  these  changes,  although 
it  is  not  sensible  to  the  thermometer.  It  performs  work  by 
overcoming  the  cohesion  of  the  molecules,  and  disappears  as 
heat.  It  is,  however,  capable  of  re-appearing  as  heat;  for, 
when  the  vapors  change  to  liquids  or  the  liquids  to  solids, 
the  force  of  cohesion  performs  work,  and  a  ^corresponding 
amount  of  heat  is  given  out.  The  heat  which  a  body 
absorbs  or  gives  out  in  changing  its  molecular  condition  is 
termed  latent  heat. 

320.  The  latent  heat  of  fusion  may  be  determined  by 
the  method  of  mixtures.  Suppose  a  pound  of  water  at  212° 
F.  be  mixed  with  a  pound  of  water  at  32°  F.,  it  will  give 

212°  ..I   S2° 
two  pounds  of  water  at  -    ^p  -  =  122°  F.  ;    but,  if  a 

pound  of  water  at  212°  F.  be  mixed  with  a  pound  of  ice  at 
32°  F.,  we  shall  have  two  pounds  of  water  at  51°  F.  In 
this  case  the  water  has  lost  212° —  51°  =  161°  F.,  while  the 
ice  has  gained  51°  —  32°  =19°  F. ;  so  that  161°—  19°  = 
142°  F.  have  disappeared  in  changing  ice  to  water;  or,  in 
other  words,  142  thermal  units  are  required  to  change  a 
pound  of  ice  into  water. 

Latent  Seat  of  Fusion. 

Water 142°.65  F. 

Sulphur 16.85 

Lead 9.65 

Mercury 5.11 


212  ELEMENTS  OF  PHYSICS. 

The  latent  heat  of  water  is  of  the  greatest  value  in  nature, 
because  (1)  it  retards  the  melting  of  snows.  If  it  were  not 
for  this  provision,  the  inhabitants  of  northern  valleys  would 
be  subject  to  terrific  inundations  at  every  approach  of  spring. 

(2)  The  melting  of  ice  withdraws  heat  from  surrounding  ob- 
jects.   Near  the  Great  Lakes,  the  spring  is  so  much  retarded 
by  the  melting  of  the  winter's  ice  .that,  generally,  the  buds  of 
trees  do  not  swell  until  the  danger  of  late  frosts  is  past. 

(3)  The  freezing  of  water  mitigates  the  sudden  setting  in 
of  frosts,  as  the  very  act  of  freezing  liberates  heat.     Hence, 
it  is  a  common  remark  that  the  weather  moderates  on  a  fall 
of  snow. 

321.  Freezing  mixtures  depend  on  the  latent  heat  which 
is  absorbed  in  dissolving  solids.     If  one  part  of  common 
salt  and  two  of  snow  are  mixed  together,  the  salt  causes  the 
snow  to  melt  and  the  water  dissolves  the  salt,  so  that  both 
become  liquid  and  absorb  a  large  amount  of  heat  from  sur- 
rounding objects.     The  temperature  may  be  lowered  to — 4° 
F.     This  is  the  mixture   used  in  freezing  ice-creams.     If 
crystallized  calcium   chloride  be  mixed  with  snow,  a  cold 
of —  50°  F.  may  be  produced.     This  is  more  than  sufficient 
to  freeze  mercury. 

322.  The  latent  heat  of  vapors  may  be  determined  by 
distilling  them  and  noting  the  rise  of  temperature  caused 
in  the  water  surrounding  the  worm  on  condensing  a  known 
weight  of  vapor.     The  following  experiment  is  a  convenient 
method  of  illustrating  the  latent  heat  of  water. 

Arrange  a  glass  flask  and  beaker,  as  in  Fig.  182.  Pour 
one  ounce  of  water  at  32°  F.  into  the  flask,  and  5J  ounces 
at  the  same  temperature  into  the  beaker.  Now,  note  (1) 
the  time  required  to  raise  the  water  in  the  flask  to  boiling 
and  that  required  to  change  the  boiling  water  into  steam. 
The  latter  will  be  5 J  times  longer  than  the  former.  (2)  When 


LATENT  HEAT  OF  VAPORS.  213 

the  water  in  the  flask  has  been  expelled,  that  in  the  beaker 
be  raised  to  212°  F.,  showing  that  an  ounce  of  steam 


FIG.  182. 

is  competent  to  raise  5J  ounces  of  steam  through  180°  F. 
Therefore,  the  latent  heat  of  steam  is  180  X  &i  =  960°. 

Latent  Seat  of  Vapors. 

Water     .....     966°.6F.  Ether     ....     162°.8  F. 
Alcohol.     .     .     .       374.9      Bisulphide  of  Carbon  156. 
Acetic  acid       .     .       183.4      Bromine      ...       82. 

323.  When  liquids  are  evaporated  they  absorb  heat 
from  surrounding  objects  and  produce  cold.  A  shower  of 
rain  cools  the  air  by  its  evaporation.  The  more  rapid  the 
evaporation  the  greater  will  be  the  effect  produced.  Water 
may  be  frozen  by  its  own  evaporation,  by  placing  a  thin, 
shallow  capsule,  filled  with  water,  over  strong  sulphuric 
acid,  under  the  receiver  of  an  air-pump.  On  rapidly  ex- 
hausting the  receiver,  the  sulphuric  acid  absorbs  the  aqueous 
vapor,  and  allows  a  very  rapid  evaporation  of  the  water, 
which  effects  the  freezing  of  a  portion  of  it. 

If  a  volatile  liquid  like  ether  or  bisulphide  of  carbon  be 
poured  in  a  watch-glass  which  rests  on  a  drop  of  water 
placed  on  a  board,  and  a  rapid  current  of  air  be  blown 


214  ELEMENTS  OF  PHYSICS. 

over  it,  the  cold  produced  by  the  evaporation  will  freeze  the 
watch-glass  to  the  board. 

324.  When  vapors  are  condensed  they  give  out  their 
latent  heat.  Water  may  be  boiled  in  a  wooden  tank  by 
forcing  steam  into  it.  Buildings  are  warmed  by  the  heat 
of  steam  generated  in  a  boiler  placed  in  the  basement.  To 
this  end,  the  steam  is  conveyed  to  the  several  apartments  by 
coils  of  iron  pipes. 

RECAPITULATION. 

The  measurement  of  heat  may  regard, 

1.  The  relative  intensity Temperature. 

2.  The  relative  quantity Specific  heat. 

3.  The  amount  absorbed  or  emitted   during  molecular 

changes  Latent  heat. 


THE  DISTRIBUTION  OF  HEAT. 

325.  The  effects  of  heat  thus  far  considered  have  refer- 
ence only  to  the  molecular  motions  which  take  place  within 
a  heated  body ;  we  are  now  to  consider  how  heat  may  be 
transferred  to  other  bodies.  In  the  first  place,  we  remark 
that  no  body  is  known  to  exist  at  a  temperature  of  absolute 
zero;  that  is,  at  a  temperature  in  which  its  molecules  are 
absolutely  at  rest  with  respect  to  each  other.  Hence,  all 
bodies  possess  some  heat.  In  the  second  place,  we  notice 
that  any  body  assumes,  sooner  or  later,  the  temperature  of 
surrounding  bodies.  Now,  this  can  occur  only  by  a  con- 
tinued exchange  of  molecular  motions,  by  virtue  of  wrhich 
every  body  emits  thermal  waves  or  vibrations  of  some  degree 
of  intensity,  while,  at  the  same  time,  it  receives  other  ther- 
mal waves  from  surrounding  bodies.  If  the  sum  of  the 


TRANSFER  OF  HEAT.  215 

motions  received  is  less  than  that  emitted,  the  body  becomes 
colder;  but,  if  greater,  the  body  becomes  warmer.  If  it 
receives  back  just  as  much  heat  as  it  gives  out,  it  remains 
at  a  uniform  temperature. 

326.  Heat  may  be  transferred  from  one  body  to  another 
in  three  ways : 

1.  By  conduction,  or  from  molecule  to  molecule. 

2.  By  convection,  or  by  molecules  moving  in  currents. 

3.  By  radiation,  or  by  thermal  undulations  through  space. 

327.  The  conductibility  of  solids  may  be  shown  by 
equal -sized   rods,   along   which  a   number  of  marbles   are 
fastened,  at   equal  distances, 

with  wax.  Fig.  183.  If  one 
end  of  the  rod  be  in  contact 
with  a  heated  body,  the  mar- 
bles will  drop  off  one  after 
the  other  as  the  different  sec- 
tions of  the  rod  attain  the  FlG-  183- 
temperature  of  the  fusing  point  of  wax.  Different  sub- 
stances will  show  different  conducting  power,  but  in  all 
cases  it  will  be  found  that  the  transference  of  heat  by  con- 
duction is  a  process  comparatively  slow.  Porous  solids  are 
poor  conductors;  liquids  and  gases  almost  non-conductors; 
many  of  the  metals  are  good  conductors. 

Relative  Thermal  Conductivity. 

Silver 100.  Iron 11.9 

Copper 73.6  Lead 8.5 

Gold 53.2  Platinum 8.4 

Brass 23.6  Bismuth 1.8 

328.  That  liquids  are  poor  conductors  may  be  shown 
by  passing  the  tube  of  an  air-thermometer  through  a  funnel, 


216 


ELEMENTS  OF  PHYSICS. 


so  that  the  bulb  shall  be  just  below  the  surface  when  the 
funnel  is  nearly  filled  with  water.  Fig.  184.  Now,  if  ether 
be  poured  on  the  water  and  ignited, 
the  thermometer  will  be  but  slightly 
affected. 

329.  The  conducting  power  of  a 
body  may  be  roughly  estimated  by 
the  touch.    An  iron  rod  heated  above 
120°  F.  will  burn  the  hand,  because 
it  conveys   its    heat    rapidly  to   the 
skin,  and  if  cooled  below   0°  F.  it 
will  blister  the  lips,  because  it  con- 
veys their  heat  away  so  rapidly.    An 
oil-cloth  feels  warmer  or  cooler  than 
a  carpet  in   the  same  room  accord- 
ing as  their  common  temperature  is 
greater  or  less  than  that  of  the  skin. 
So,  also,  a  person  clad  in  woolen  gar- 
ments may  enter  an  oven  heated  to  300°  F.  without  incon- 
venience, because  both  his  garments  and   the  air  are  poor 
conductors. 

Water  is  sooner  heated  in  a  tin  cup  than  in  one  of  por- 
celain, because  the  metal  is  a  better  conductor  of  heat. 
Porous  bodies,  like  ashes  and  plaster  of  Paris,  are  such  poor 
conductors  that  if  the  hand  be  protected  by  a  thin  layer  of 
either,  it  may  carry  live  coals  without  danger. 

330.  Non-conductors    are   used    (1)    to    prevent   the 
escape  of  heat,  or  (2)  to  exclude  heat. 

1.  Double  doors  and  windows,  which  inclose  a  layer  of 
air,  prevent  the  escape  of  heat  from  our  apartments.  Cloth- 
ing prevents  the  escape  of  heat  from  our  bodies.  The  con- 
ducting power  of  the  ordinary  materials  used  is  in  this 
order:  linen,  cotton,  silk,  wool,  furs.  Hence,  with  equal 


FIG.  184. 


CONVECTION. 


217 


texture,  a   woolen  garment   is    warmer    than   one   of  silk, 
cotton,  or  linen. 

2.  Furnace  men  wear  thick  woolen  garments  to  exclude 
heat,  because  that  to  which  they  are  exposed  is  greater  than 
the  heat  of  their  bodies.  Ice  may  be  kept  from  melting  by 
wrapping  about  it  a  thick  blanket.  Ice-houses  have  double 
walls,  inclosing  a  thick  layer  of  straw,  sawdust,  or  charcoal. 
Water-coolers  are  constructed  in  the  same  manner. 

331.  Convection.     If  heat  be  applied  to  the  bottom  of 
a  flask  of  water,  (Fig.  185),  con- 
taining   matter    in    suspension,   as 

sawdust,  up  and  down  currents  will 
be  formed.  The  particles  of  the 
liquid  wThich  become  heated  ex- 
pand and  rise,  because  the  colder 
and  heavier  particles  descend  and 
force  them  upward.  This  process 
of  circulation  among  molecules  is 
termed  convection. 

332.  The  convection  of  gases 
is    more    energetic    than    that    of 
liquids,  because  their  expansion  by 
heat  is  much  greater.     If  "touch- 
paper"  containing  potassium  chlo- 
rate be  burned   in  the  vicinity  of  a  heated  body,  the  cur- 
rents of  air  arising  from  it  may  be   traced  in  the  smoke. 
The  air  which  thus  rises  is  heated  by  convection. 

• 

333.  In  all  cases  of  convection  there  must  be  two  cur- 
rents in  opposite  directions.     If  a  lighted  candle  be  held  in 
the  crack  of  a  door  which  opens  between  two  apartments  of 
different   temperatures,    a    current  of  warm   air   from    the 

heated  room  will  drive  the  flame  outward,  if  held  at  the 
PHYS.  19. 


218  ELEMENTS  OF  PHYSICS. 

top  of  the  door ;   and  a  current  of  cold  air  will  drive  the 
flame  inward,  if  held  at  the  bottom  of  the  door. 

The  winds  are  primarily  due  to  interchange  of  air  between 
localities  unequally  heated.  Only  the  lower  current  admits 
of  being  accurately  traced,  but  we  have  ample  evidence  that 
there  are  also  upper  currents.  It  frequently  happens  that 
clouds  are  seen  moving  in  different  directions — the  lower 
clouds  in  the  direction  of  the  surface-winds,  and  the  upper 
clouds  in  the  opposite  direction. 

334.  The  heat  of  the  sun  can  not  reach  the  earth  by 
conduction  nor  by  convection,  since  heat  is  propagated  by 
either  of  these  methods  very  slowly.     In  our  study  of  the 
solar  spectrum  we  learned  that  the  least  refracted  end  of 
the  spectrum  contained  invisible  rays  which  had  the  power 
of  affecting  the  thermometer.     These  dark  rays  must  reach 
us  in  the  same  way  that  light  reaches  us;  that  is,  by  ther- 
mal waves,  which   are   transmitted   by  the  aether  and  other 
media.     Heated  bodies  have  the  same   power  of  emitting 
thermal  waves  in  all  directions  that  luminous  bodies  have 
of  emitting   luminous    waves.      This    emission   of   heat    is 
termed  radiation.     The  phenomena  of  radiant  heat  and  light 
are,  in  all  respects,  similar ;  and,  with  the  necessary  change 
of  terms,  their  laws  are  identical. 

The  lawrs  of  radiant  heat  are: 

1.  Heat  radiates  in  straight  lines  in  all  directions. 

2.  The  intensity  of  radiant  Jieat  is  inversely  as  the  square  of 
the  distance  from  its  source. 

3.  The  intemity  of  radiant  heat  is  proportional  to mthe temper- 
ature of  its  source. 

335.  Radiant  heat,  incident  on  a  surface,  may  be  (1) 
reflected,  (2)  refracted,  (3)  absorbed,  or  (4)  transmitted. 

336.  Substances  which  reflect  light  well  are  also  good 


REFRACTION.  219 

reflectors  of  heat.  The  polished  metals  are  all  good  reflect- 
ors-of  heat.  Archimedes  is  said  to  have  burned  the  Roman 
fleet  at  Syracuse  by  concentrating  upon  the  ships  the  solar 
rays  by  means  of  concave  mirrors. 

337.  When  a  solar  beam  is  transmitted  through  a  prism 
of  rock-salt,  and  the  spectrum  is  examined  by  a  thermom- 
eter, we  have  the  result  sketched  in  Fig.  167,  showing : 

1.  That  the  thermal  spectrum  extends  through  and  be- 
yond the  visible  spectrum.     Thermal  waves  must,  therefore, 
be  of  different  refrangibility  and  wave  length. 

2.  The  maximum  heating  effect  lies  beyond  the  red,  in 
rays  of  great  wave  length,  but  invisible  to  the  eye. 

The  thermal  waves  which  accompany  light  are  called 
luminous  thermal  waves,  and  the  dark  rays  are  called  obscure 
thermal  waves.  When  a  platinum  wire  is  heated  it  emits,  at 
first,  only  obscure  rays  ;  when  it  becomes  incandescent,  it 
not  only  emits  luminous  rays,  but  adds  to  the  intensity  of 
the  obscure  vibrations. 

338.  Most  transparent  bodies  transmit  the  rays  of  heat 
from  the  sun  as  well  as  those  of  light,  but  will  not  equally 
transmit  the  thermal  rays  from  artificial  sources.     Thus,  the 
heat  of  the  sun  will  readily  pass  through  glass  windows  and 
warm    a    room,   while   the    same   thickness   of   glass   would 
effectually  shut  off  the  heat  of  a  fire.     On  the  other  hand, 
there  are  bodies    that  are  opaque  to  light  which  transmit 
the  dark  rays  of  heat  almost  perfectly ;    such,  for  example, 
is  a  solution   of  iodine   in    bisulphide  of   carbon.     A  sub- 
stance which    transmits  heat    is   called   diathermanous ;    one 
that  is  opaque  to  heat   is  called  athermanous.     Rock-salt  is 
one  of  the  most  diathermanous  substances  known.     A  lens 
made  of  rock-salt  will  so   concentrate  the  obscure  thermal 
rays  that  they  may  be  made  to  melt  and  even  ignite  solid 
bodies. 


220  ELEMENTS  OF  PHYSICS. 

The  incident  rays  of  heat  which  are  not  reflected  or 
transmitted  are  absorbed.  Only  the  rays  which  are  ab- 
sorbed have  any  effect  in  warming  the  body  on  which  they 
fall.  Dry  air  is  almost  perfectly  diathermanous,  but  air 
containing  moisture  has  far  less  power  of  transmitting  lumi- 
nous thermal  rays,  and  is  almost  athermanous  for  obscure 
thermal  rays.  The  solar  rays  pass  with  comparative  ease  to 
the  earth,  and  are  expended  in  warming  its  surface.  The 
heated  earth  radiates  only  obscure  rays,  which  are  absorbed 
by  the  atmosphere,  and,  consequently,  its  rate  of  cooling 
is  diminished.  In  central  Asia  the  air  is  very  dry,  and  the 
radiation  from  the  earth  is  so  rapid  that  the  nights  are 
very  cold  and  the  winters  almost  unendurable. 

The  hot-beds  of  gardeners  act  by  economizing  the  heat 
of  the  sun.  The  solar  rays  p'ass  freely  through  the  glass 
and  are  absorbed  by  the  earth  and  the  plants.  These  emit 
only  obscure  rays,  which  can  not  escape  through  the  glass. 
The  air  confined  in  the  bed  attains  a  temperature  above 
that  of  the  exterior  atmosphere. 

339.  If  a  body  is  athermanous  all  the  rays  of  heat 
which  fall  upon  it  that  are  not  reflected  are  absorbed. 
Hence,  bad  reflectors  are  good  absorbents  and  are  readily 
warmed.  As  bodies  must  give  out,  in  cooling,  the  heat 
which  they  have  absorbed,  so  good  absorbents  are  good  radi- 
ators. The  relation  between  the  radiating,  reflecting,  and 
absorbent  powers  will  be  seen  by  the  following  table : 

Reflection.       Absorption.       Radiation. 

Lamp-black 0  100  100 

Indian  ink 4  96  85 

White  lead 47  53  100 

Isinglass 48  52  91 

Gum  lac 57  43  72 

Polished  metal .  86  14  12 


RADIATING  POWER.  221 

The  radiating  power  of  a  body  is  dependent  more  on 
the  nature  of  its  surface  than  of  its  substance.  If  a  tin  can- 
ister have  one  of  its  sides  coated  with  lamp-black,  another 
with  paper,  a  third  scratched  or  tarnished,  and  the  fourth 
polished,  and  be  filled  with  boiling  water,  its  sides  will,  of 
course,  have  the  same  temperature;  but  they  will  differently 
affect  a  thermometer  placed  in  succession  near  each  face, 
according  to  the  difference  in  their  radiating  power. 

Lamp-black  has  the  highest  emissive  power  known;  the 
polished  metals  are  the  poorest  radiators.  Hence,  a  bright 
silver  tea-pot  filled  with  hot  water  will  retain  its  tempera- 
ture longer  than  one  of  earthenware. 

340.  Franklin  found  by  placing  pieces  of  cloth  of  the 
same  texture,  but  of  different  colors,  upon  newly  fallen 
snow,  that  the  snow  melted  under  the  cloth  with  greater 
rapidity  the  darker  the  tint.  This  fact  shows  that,  for  solar 
rays,  clothes  of  dark  color  are  better  absorbents  and  poorer 
reflectors  than  white.  Other  experiments  show  that  this 
difference  in  the  absorptive  effect  of  colors  entirely  fails  for 
heat  from  artificial  sources.  It  so  happens  that  many  good 
reflectors  are  white,  and  many  good  absorbents  and  radiators 
are  dark ;  but  their  respective  powers  are  due  rather  to  the 
molecular  condition  of  their  surfaces  than  to  their  colors. 


RECAPITULATION. 

f   Conduction. 

Heat  may  be  transferred  by  I    Convection. 

(    Radiation. 

{Reflected. 
Absorbed. 
Refracted. 
Transmitted. 


222  ELEMENTS  OF  PHYSICS. 


THE    SOURCES    OF   HEAT. 

341.  The  sources  of  heat    may  be    comprised    in    three 
classes:  (1)  physical,  (2)  chemical,  (3)  mechanical. 

The  principal  physical  sources  are  the  sun  and  the 
fixed  stars.  It  has  been  calculated  that,  if  the  earth  had 
no  atmosphere,  the  solar  heat  received  by  the  earth  in  one 
year  would  melt  a  layer  of  ice,  completely  enveloping  it,  to 
the  depth  of  one  hundred  feet.  It  has  also  been  estimated 
that  the  earth  receives  from  the  fixed  stars  about  four-fifths 
of  this  amount.  These  are  the  ultimate  sources  of  most  of 
the  available  heat  of  the  globe.  Were  either  of  these  cut 
off,  the  life  of  the  globe  would  soon  be  destroyed. 

342.  When  any  two  bodies  unite  in  chemical  combina- 
tion heat  is  usually  evolved.     Combustion  is  the  rapid  com- 
bination of  two  or  more  substances,  attended  by  the  evolu- 
tion of  heat,  and  generally  of  light.     If  a  grain  of  iodine 
l)e  placed  on  a  slip  of  phosphorus  they  will  kindle  into  a 
flame,  which  will  afterward  be  continued  by  the  oxygen  of 
the  air. 

343.  Ordinary  combustion  is  due  to  the  union  of  the 
oxygen  of  the  air  with  the  carbon  and  hydrogen  contained 
in  the  coals,  oils,  and  gases  of  our  fires  and  flames.      The 
rusting  of  iron  and  the  decay  of  wood,  are  examples  of  slow 
combustion    with    oxygen.      A    log    of   wood    in    decaying 
evolves  the  same  amount  of  heat  that  it  does  in  burning, 
although  the  combustion  takes  place  so  slowly  that  no  in- 
crease in  temperature  is  perceptible. 

Animal  heat  is  due  to  slow  combustion.  In  respiration  (1) 
oxygen  passes  by  osmosis  through  the  cell  walls  of  the  lungs, 
and  is  absorbed  by  the  blood ;  (2)  this  blood  is  then  carried 


MECHANICAL  SOURCES  OF  HEAT.  223 

to  the  capillaries  of  the  different  organs,  where  the  oxygen 
unites  with  the  carbon  of  the  tissues  and  forms  carbonic 
acid ;  (3)  the  blood  then  returns  to  the  lungs  charged  with 
this  carbonic  acid;  (4)  the  carbonic  acid  is  then  exhaled  by 
osmosis,  and  a  fresh  supply  of  oxygen  absorbed. 

The  supply  of  carbon  in  the  tissues  is  maintained  by  the 
processes  of  digestion  and  nutrition.  Thus,  in  one  sense,  our 
animal  heat  is  maintained  by  the  indirect  combustion  of 
food  and  air. 

344.  The  mechanical  sources  of  heat  are  percussion, 
compression,  and  friction.  (1)  If  a  nail  be  pounded  on  an 
anvil  with  rapid  blows,  it  may  be  made  red-hot  by  percus- 
sion. (2)  The  production  of  heat  by  the  compression  of 
gases  may  be  shown  by  the  pneumatic  syringe,  Fig.  186. 


FIG.  186. 

This  instrument  consists  of  a  stout  tube  in  which  a  piston 
works  air-tight.  To  use  it,  a  piece  of  tinder  is  placed  on  the 
bottom  of  the  piston,  which  is  then  driven  suddenly  down 
the  tube.  The  air  in  the  tube  is  compressed,  and  liberates 
so  much  heat  as  to  set  fire  to  the  tinder,  which  is  seen  to 
burn  when  the  piston  is  withdrawn. 

(3)  The  friction  of  two  bodies  always  produces  heat.  It 
is  the  heat  produced  by  friction  that  ignites  the  phosphorus 
on  the  end  of  a  match,  and  that  causes  the  axles  of  car- 
wheels  to  become  hot.  Savages  procure  fire  by  revolving 
the  end  of  one  piece  of  wood  in  the  cavity  of  another. 

An  experimental  demonstration  of  the  same  fact  n  Ay  be 
shown  by  attaching  to  a  whirling  table  a  brass  tube  filled 
with  water,  and  corked.  Fig.  187.  If,  when  the  tube  is 
revolving  rapidly,  a  clamp,  P,  of  two  pieces  of  oak  is 


224 


ELEMENTS  OF  PHYSICS. 


pressed  against  the  tube,  the  heat  evolved  by  the  friction 
of  the  clamp  will  be  sufficient  to  boil  the  water  in  a  few 
minutes. 


FIG.  187. 

345.  These  facts  are  in  accordance  with  the  dynamical 
theory  of  heat,  which  assumes  that  heat  is  a  kind  of  energy 
which  produces  molecular  motion.  In  all  cases  of  percus- 
sion, compression,  and  friction,  a  certain  amount  of  mechan- 
ical energy  is  arrested,  and  its  visible  motion  is  destroyed. 
At  the  same  time  heat  is  produced.  That  is,  the  energy  of 
visible  motion  is  transformed  into  the  energy  of  molecular  motion, 
which  is  heat. 

Conversely,  heat  is  consumed  in  effecting  mechanical  work. 
Let  a  cylinder  filled  with  compressed  air  be  cooled  to  the 
temperature  of  surrounding  bodies.  Its  elastic  force  is  com- 
petent to  perform  mechanical  work  (1)  by  moving  a  pis- 
ton, and  (2)  by  displacing  the  air  in  front  of  the  piston. 
If  the  air  be  allowed  to  expand  so  as  to  perform  work,  it 
will  be,  at  the  same  time,  chilled,  because  its  molecular 
energy  is  transformed  into  the  energy  of  visible  motion. 


JOULE'S  EQUIVALENT.  225 

346.  There  is  a  constant  numerical  relation  between 
the  energy  of  visible  motion  and   the  energy   of  molecular 
motion,  which   is   known   as  Joule's   equivalent,  and   is  thus 
expressed  :  The  amount  of  heat  required  to  raise  one  pound 
of  water  1°  F.  is  competent  to  lift  772  pounds  one  foot  high. 
The   converse  is  also  true ;    if  772  pounds  be  dropped  one 
foot  it  will   develop  sufficient  heat  to  raise  one  pound  of 
water  1°  F. 

347.  If  we   know  the   weight   and  velocity  of  any 
moving  body,  we  can  calculate  the  amount  of  heat  which 
would  be  generated  by  suddenly  stopping  it.     It  has  been 
calculated   that  if  the  earth   were  stopped  in  its  orbit,  it 
would  develop  heat  equal  to  that   derived  from  the  com- 
bustion  of  fourteen  equal -sized  globes  of  coal.     If,  then, 
it  should  fall  into  the  sun,  it  would  generate  by  the  collision 
heat  equal  to  that  evolved  by  the  combustion  of  5,600  equal 
worlds  of  solid  carbon. 

These  considerations  have  led  some  philosophers  to  the 
conclusion  that  the  solar  heat  is  maintained  by  the  falling 
of  meteoric  masses  into  the  body  of  the  sun.  If  the  earth 
should  strike  the  sun,  the  heat  developed  by  the  shock 
would  be  sufficient  to  equal  the  solar  radiation  for  a 
century. 

348.  The  dynamical  theory  of  heat  also  explains  the 
phenomena  of  expansion  and  of  latent  heat.     Thus,  when 
heat  enters  a  body,  its  actual   energy  is  employed  (1)  in 
increasing  the  intensity  of  molecular  motion,  which  is  shown 
by  a  rise  in  the  temperature ;    (2)    this  also  separates  the 
molecules  and  produces   expansion ;     (3)    a    sufficient    heat 
melts  or  vaporizes  the  body.     The  latent  heat  required  is 
the  energy  necessary  to  overcome  cohesion ;   that  is,  it  per- 
forms work  in  separating  and  re-arranging  the  position  of  the 
molecules.     The  latent  heat  which  disappears  is  not  lost, 


226  ELEMENTS  OF  PHYSICS. 

but  has  been  employed  in  giving  the  molecules  new  posi- 
tions. If  the  vapor  returns  to  the  liquid  state,  or  a  liquid 
to  the  solid  state,  an  equal  amount  of  heat  will  be  given 
out,  because  interior  work  has  been  performed  by  cohesion, 
which  draws  the  molecules  closer  together,  and  is  trans- 
formed into  sensible  heat. 

We  may  roughly  compare  latent  heat  with  mechanical 
energy.  If  I  throw  a  stone  to  a  roof  sixteen  feet  high,  I 
shall  need  to  give  to  it  a  velocity  of  thirty-two  feet  per 
second.  While  the  stone  rests  on  the  roof  it  produces  only 
pressure,  but  it  is  evident  that  should  it  fall,  it  will  again 
attain  a  velocity  of  thirty-two  feet  per  second  before  it 
strikes  the  ground.  Therefore,  the  stone,  while  on  the  roof, 
has  a  possible  energy  due  to  its  position.  So,  also,  if  I  melt 
a  body  I  shall  require  to  expend  a  certain  amount  of  sensi- 
ble heat;  but,  in  so  doing,  I  shall  confer  upon  the  mole- 
cules a  possible  or  potential  energy  of  position,  which  will  be 
again  transformed  into  the  sensible  energy  of  heat  when  the 
melted  body  solidifies. 

349.  Force  may  be  changed  but  not  annihilated. 
The  sun  is  the  ultimate  source  of  the  available  forms  of 
energy  with  which  we  are  surrounded.  Let  us  consider  a 
few  of  the  ways  by  which  sunshine  may  be  transmuted  and 
preserved. 

1.  The  mechanical  energy  of  the  winds,  of  falling  water, 
and  of  running  streams,  is  due  to  the  joint  action  of  gravi- 
tation and  of  the  solar  heat.     A  part  of  this  energy  may  be 
made  to  re-appear  as  heat  by  friction.     Thus,  a  large  room 
has  been  warmed  by  the  friction  of  two  plates,  made  to  re- 
volve by  machinery  driven  by  a  fall  of  water. 

2.  Plants  grow  by  reason  of  the  light  and  heat  of  the 
sunshine,  and  accumulate  a  supply  of  fuel  and  of  food. 

(a.)    Wood  and  mineral  coal  are,  therefore,  transmuted 


CONSERVATION  OF  FORCE.  227 

sunshine.     In  combustion,  the  heat  re-appears  as  heat,  or  it 
may  be  applied  as  a  moving  force  for  engines. 

(6.)  Food  is  transmuted  by  animals  into  animal  heat  and 
muscular  energy,  or  stored  up  as  flesh.  Beef  and  mutton 
are,  therefore,  due  to  solar  rays  twice  transmuted. 

RECAPITULATION. 

The  sources  of  heat  are— 

1.  Physical j  The  sun. 

(  The  fixed  stars. 

2.  Chemical Combustion. 

C  Compression. 

3.  Mechanical •<  Percussion. 

(.  Friction. 

PROBLEMS. 

1.  How  much  will    a   railway  track  100   miles   long   expand  on 
being  heated  from  32°  F.  to  96°  F.  ? 

2.  How  many  thermal   units   are   required  to  raise  80  pounds  of 
water  from  32°  F.  to  212°  F.?    Suppose  a   pound  of  coal,  if  econom- 
ically  burned,  to  have  this   thermal   power,  how  many  pounds  of 
mercury  can  it  raise  through  the  same  temperature? 

3.  How  many  pounds  of  ice  at  32°  F.  would  the  same  fuel  melt? 
How  many  pounds  of  water  at  212°  F.  would  it  change  into  steam? 

4.  From   the   table   on   page   199  calculate  the  relative  lengths  of 
silver  and  platinum  which  should  be  taken  to  construct  a  gridiron 
pendulum. 


CHAPTER  XVI. 

ELECTRICITY. 

350.  One  of  the  earliest  physical  facts  recorded  in  the 
history  of  science,  is  that  when  amber  is  rubbed  with  silk, 
it  acquires  the  property  of  attracting  to  itself  light  bodies, 
and  then  of  repelling  them.     Within  the  past  century,  phi- 
losophers have  found  that  these  are  but  particular  manifesta- 
tions of  a  force  which  is  constantly  evoked  in  all  kinds  of 
molecular  changes,  and   whose   phenomena  are  among  the 
most  wonderful  in   nature.     This  force   is  electricity.     It   is 
convenient  to  study  its  phenomena  under  three  divisions : 
(1)    Magnetism,    (2)    Statical    Electricity,    (3)    Dynamical 
Electricity. 

THE  PHENOMENA  OF  MAGNETISM. 

351.  It  has  long  been  known  that  a  certain  ore  of  iron, 
called   the   loadstone,  has    the    property  of  attracting   iron 
filings.     Because  this  ore  was  first  found  near  Magnesia,  a 
city  of  Asia  Minor,  loadstones   are  called  natural  magnets. 
Bars  of  hardened  steel  may  be  converted  into  artificial  mag- 
nets far  more  powerful  than  natural  magnets. 

352.  If  a  magnet  be  rolled  in  iron  filings,  the  filings 
will  cling  to  it,  but  especially  at  the  ends.     Fig.  188.     These 

ends  are  termed  the  poles  of  the  mag- 
net. The  force  residing  in  a  magnet 
is  called  magnetism. 

FIG-  188.  If  a   sheet   of  stiff  paper   be   laid 

upon  a  bar  magnet,  and  iron  filings  be  sifted  evenly  upon 

(228) 


MAGNETISM. 


229 


the  paper,  the  particles  of  iron  will  arrange  themselves  in 
curved  lines  about  the  poles.  Fig.  189.  If  a  magnetic  bar 
or  needle  be  poised  at  its  center  so  that  it  will  swing  freely, 


FIG.  189. 

one  end  will  point  toward  the  north  and  the  other  toward 
the  south ;  hence,  one  end  is  called  the  south  and  the  other 
the  north  pole  of  the  magnet. 

353.  Either  pole  will  equally  attract  iron  filings;  but 
if  two  magnets  are  brought  near  each  other,  it  will  be  found 
that  the  north  pole  of  one  will  attract  the  south  pole  of  the 
other.     If,  however,  two  sim- 
ilar   poles    are    brought    near 

each  other,  a  repulsion  takes 
place.  Fig.  190.  Hence,  this 
law :  Like  poles  repel  and  unlike 
poles  attract  eacJi  other. 

354.  If  a  long  steel  needle 
be  magnetized,  the  center  will 
exhibit  no  magnetic  force  and 
is  said  to  be  neutral.     If  the 
needle   be  broken,   each   half 
will  be  found  to  be  a  magnet 

with  two  equal  and  opposite  poles.  If  this  division  be  con- 
tinued, no  portion  can  be  obtained  so  small  that  it  will  not 
be  a  perfect  magnet.  We,  therefore,  conclude  that  every 


FIG.  190. 


230 


ELEMENTS  OF  PHYSICS. 


magnet  is  a  collection  of  polarized    particles  having  their 
similar  poles  turned  in  the  same  direction. 

We  may  represent  this  state  of  polarity  in  a  magnet  by 
Fig.  191,  in  which  the  alternate  black  and  white  spaces 


FIG.  191. 

represent  the  polarity  of  each  particle.  All  the  north  poles 
are  disposed  in  one  direction  (the  black  spaces)  and  all  the 
south  poles  (the  white  spaces)  in  the  opposite.  The  opposite 
polarities  balance  each  other  at  the  center,  which  thus  re- 
mains neutral,  but  are  strongly  manifested  at  the  ends. 

355.   If  a  rod  of  soft  iron,  Fe,  Fig.  192,  be  brought 
near  one  of  the  poles  of  a  magnet,  M,  the  two  ends  of  the 
N>_Fe_&         N  M  S 


FIG.  192. 

rod  will  also  be  able  to  attract  iron  filings.  The  rod  becomes 
a  temporary  magnet,  but  it  will  lose  its  magnetic  properties 
soon  after  it  is  taken  away  from  the  presence  of  the  magnet. 
The  influence  by  virtue  of  which  a  magnet  can  develop 
magnetism  in  iron  is  called  induction.  We  may  suppose 
that,  in  its  ordinary  state,  the  molecules  of  the  iron  rod  are 
all  indued  with  magnetism,  but  that  they  are  so  arranged 
that  the  opposite  forces  neutralize  each  other ;  and  that  the 
presence  of  the  magnet  in  some  way  so  modifies  the  sur- 
rounding region  that  the  molecules  of  the  iron  assume  the 
polarized  state  of  the  magnet  as  represented  in  Fig.  191. 
The  inductive  force  is  greatest  when  the  magnet  is  in  con- 
tact with  the  iron.  If  a  steel  bar  be  in  contact  with  a 
magnet,  its  particles  become  polarized  very  slowly;  but 


MAGNETS.  231 

when  once  acquired,  its  magnetism  is  permanent.  Magnet- 
ism may  be  sooner  induced  in  steel  by  rubbing  it  with  one 
of  the  poles  of  a  magnet.  In  this  way  the  ordinary  mag- 
netic needles  are  prepared,  but  the  more  powerful  magnets 
are  produced  by  means  of  the  voltaic  current,  as  will  be 
described  hereafter.  It  is  important  to  notice  that  in  in- 
duction there  is  no  transfer  of  any  force,  but  merely  a  devel- 
opment of  polarity  among  the  particles  of  the  body  acted 
upon. 

A  magnetic  battery  consists  of  a  number  of  magnets  joined 
together  with  their  similar  poles  in  contact.  The  common 
form  is  that  of  a  horse-shoe.  Fig.  193.  When 
a  magnet  exerts  its  inductive  power  on  a  piece 
of  soft  iron,  its  own  magnetic  intensity  is  tem- 
porarily increased.  Fer  this  reason  the  mag- 
net is  provided  with  a  keeper  or  armature,  K, 
of  soft  iron. 


356.   Iron,  steel,  nickel,  and  cobalt  are 

the  only  substances  in  which  magnetism  can 
be  developed  by  ordinary  induction.  Man- 
ganese and  a  few  other  substances  are  also 
attracted  by  very  powerful  magnets.  All 
these  are  called  magnetic  substances.  If  a  FIG.  193. 
magnetic  substance  is  suspended  by  a  string  between  the 
poles  of  a  horse-shoe  magnet  it  will  take  a  position  in  the 
direction  of  the  line  which  joins  the  two  poles  of  the 
magnet. 

On  the  other  hand,  there  are  a  great  number  of  sub- 
stances which,  if  similarly  suspended,  will  assume  a  position 
at  right  angles  to  the  line  joining  the  poles,  as  if  repelled 
by  them.  Such  substances  are  called  diamagnetic.  Among 
diamagnetic  substances  are  phosphorus,  bismuth,  antimony. 
The  diamagnetism  is  not  permanent. 


232  ELEMENTS  OF  PHYSICS. 

357.  The  earth,  acts  as  a  magnet.  The  magnetic 
needle,  which  is  of  almost  priceless  value  to  mariners,  points 
toward  the  magnetic  poles  of  the  earth.  These  magnetic 
poles  are  near,  but  do  not  coincide  with  the  geographical 
poles  of  the  earth.  Hence,  the  needle  will  point  in  a  due 
north  and  south  line  only  when  the  magnetic  meridian  coin- 
cides with  the  geographical  meridian.  This  is  very  nearly 
the  case  at  Cleveland,  O.,  but  in  New  York  the  needle 
points  west  of  north  and  in  Chicago  east  of  north.  More- 
over, the  magnetic  poles  are  slowly  shifting  their  position 
westward,  so  that  the  magnetic  meridian  does  not  remain 
constant.  The  deviation  of  the  needle  from  the  geograph- 
ical meridian  is  called  the  decimation  of  the  needle. 

RECAPITULATION. 

f   Natural  or  artificial. 
Magnets  are     .     .      ] 

(   Permanent  or  temporary. 

f   Attracted  by  magnets  are    .     .    Magnetic. 
Substances    ...      <    _       „   ,    , 

I    Repelled   by   magnets  are    .     .    Diamagnetic. 


THE  PHENOMENA  OF  STATICAL  ELECTRICITY. 

358.  An  electric  pendulum  is  a  pith  ball  attached,  by  a 
silk  thread,  to  a  glass  support.  If  a  stick  of  sealing-wax 
be  rubbed  with  dry  flannel  and  brought  near  the  pith  ball, 
Fig.  194,  the  latter  is  instantly  attracted,  but  is  soon 
repelled.  If,  now,  a  warm  glass  rod  be  rubbed  with  a 
silk  handkerchief  and  presented  to  the  ball,  the  same  phe- 
nomena of  attraction  and  repulsion  will  be  observed. 

It  will  now  be  found   that  when   the  ball  has  been  re- 


STATICAL  ELECTRICITY. 


233 


FIG.  194. 


pelled  by  the  glass,  it  will  be  attracted  by  the  wax ;  and 
when  again  repelled  by  the  wax,  it  will  be  attracted  by  the 
glass.  If  the  glass  and  wax  be  placed  on  opposite  sides  of 
the  ball,  it  will  vibrate  between  them  by  the  alternate 
attraction  and  repulsion  of 
each.  It  is,  therefore,  evi- 
dent that  the  glass  and  wax 
manifest  similar  and  yet  op- 
posed properties.  These  prop- 
erties, thus  excited  by  fric- 
tion, are  due  to  electricity. 

359.  Electricity  is  a  force 
which    becomes   manifest  by 
its  peculiar  phenomena  of  at- 
traction and  repulsion.     It  is 
now  regarded  as  a  mode  of 

molecular  motion  which  is  always  manifested  in  two  opposite 
or  polarized  states.  That  developed  on  the  glass  is  called 
positive,  (+),  and  that  on  the  wax,  negative  electricity,  ( — ). 
Formerly,  electricity  was  supposed  to  be  due  to  the  presence 
or  absence  of  a  single  electrical  fluid,  or  to  the  presence  of 
two  electrical  fluids.  There  is,  however,  no  evidence  of  the 
existence  of  any  electrical  fluid.  Nevertheless,  many  of  the 
terms  of  the  fluid  theory  are  still  in  common  use,  and  are 
convenient  for  describing  most  electrical  phenomena,  although 
the  meaning  attached  to  them  is  taken  in  a  sense  different 
from  that  originally  intended. 

360.  In  the  preceding  experiment  we  suppose  that  the 
wax  became  negatively  electrified  by  friction,  and,  on  con- 
tact, transferred  a  portion  of  this   force   to  the  ball.     The 
ball   thereby  became   electrified    or  charged   with    negative 
electricity  and  the  two  bodies  separated.     On  bringing  the 

charged  ball  near  the  positively  electrified  glass  the  two 
PHVS.  20. 


234  ELEMENTS  OF  PHYSICS. 

were  attracted,  because  of  their  different  electrical  states. 
The  glass  then  communicated  enough  of  positive  electricity 
to  neutralize  the  negative  electricity  of  the  ball,  and,  also, 
to  render  it  positively  charged.  The  ball  was  then  repelled 
by  the  glass  and  attracted  by  the  wax,  and  so  on  through  a 
series  of  attractions  and  repulsions.  From  these  experi- 
ments we  derive  the  following  law :  Two  bodies  charged  ivith 
like  electricities  repel  each  other;  two  bodies  charged  with  opposite 
electricities  attract  each  other. 

361.  Electricity  is  transmitted  from  one  body  to  an- 
other with  different  degrees  of  rapidity.  Those  substances 
that  transmit  electricity  readily  are  called  conductors;  those 
that  do  not,  are  called  non-conductors  or  insulators.  In  the 
following  list  the  substances  named  are  arranged  in  the 
order  of  their  conducting  power.  Those  midway  in  the  list 
may  be  termed  semi-conductors  or  semi-insulators. 

Conductors.  Semi-conductors. 

1.  The  metals,  7.  Ether,  13.  Furs, 


'2.  Charcoal, 
3.  Graphite, 
4.  Acids, 
5.  Water, 

8.  Dry  wood, 
9.  Paper, 
10.  Dry  ice, 
11.  Caoutchouc, 

14.  Silk, 
15.  Glass, 
16.  Wax, 
17.  Shellac, 

6.  Linen,  12.  Air  and  gases,    18.  Ebonite. 

Semi-iusulators.  Insulators. 


362.  In  order  that  a  charged  body  may  retain  its 
electrical  force,  it  must  either  be  a  non-conductor,  or  be 
imulated  by  being  supported  on  non-conductors.  The  most 
common  insulators  are  made  of  glass.  Baked  wood  covered 
with  shellac  varnish  will  answer  very  well.  Dry  air  is 
necessary  for  insulation.  In  a  damp  room  a  film  of  moist- 
ure gathers  upon  the  apparatus  and  forms  a  conducting 
surface. 


ELECTROSCOPE.  235 

363.  Electricity  is  produced  whenever  two  dissimilar 
substances  are  rubbed  together.      The  reason  why  it  is  not 
more  frequently  manifest  is  because  it  is  carried  off  as  fast 
as  it  is  developed.     When  the  electrical  force   is   sufficient 
to  force  its  way  through   a  bad   conductor  a  spark  may  be 
produced.      In   dry,   frosty  weather,  a   person,  by  shuffling 
about  a  warm,  carpeted  room,  may  develop  electricity  suffi- 
cient to  emit  a  spark  from  his  finger  capable  of  igniting  a 
jet  of  gas. 

364.  Both  kinds  of  electricity  are  always  simultane- 
ously produced.     If  two  insulated  disks  of  dry  wood,  one 
covered  with   shellac  and  the   other  with  silk,  are  rubbed 
together  and   separated,  the   shellac  will  manifest  positive 
and  the  silk,  negative  electricity.      Any  substance  in  the 
following  list,  when   rubbed  by  any  one   succeeding  it,  be- 
comes positively  electrified,  and  by  any  one  preceding  it, 
negatively  electrified : 

-f-  Cat's-fur,  flannel,  smooth  glass,  cotton,  paper,  silk,  the 
hand,  sealing-wax,  rough  glass,  sulphur,  ebonite,  — . 

Thus  paper  becomes  positively  electrified  when  rubbed 
with  silk  and  negatively  electrified  when  rubbed  with 
flannel. 

385.  The  electricity  which  is  produced  by  friction  is 
called  frictional  electricity.  There  are,  however,  other  modes 
of  producing  the  same  electrical  phenomena.  It  is  also 
called  statical  electricity,  because  it  may  be  retained  for  a 
time  upon  an  insulated  body. 

An  electroscope  is  an  instrument  used  to  detect  the  presence 
arid  determine  the  kind  of  electricity  in  any  body. 

The  simplest  is  some  form  of  the  electric  pendulum.  The 
gold-leaf  electroscope,  Fig.  195,  consists  of  two  strips  of 
gold-leaf,  suspended  in  a  glass  vessel  by  means  of  a  metallic 
rod  which  terminates  in  a  knob  or  a  plate.  Within  the 


236 


ELEMENTS  OF  PHYSICS. 


vessel  are   two   metallic   posts   connected  with   the  ground, 
which  serve  to  remove  an  excessive  charge  from  the  leaves. 

If  the  knob  be  touched  with 
an  electrified  glass  rod,  the 
leaves  will  diverge,  because 
they  become  charged  with  pos- 
itive electricity.  If,  now,  any 
electrified  body  be  brought 
near  the  knob,  the  kind  of 
electricity  in  the  body  may 
be  determined  by  its  influence 
on  the  gold-leaves ;  for,  if  the 
electricity  be  positive,  the 
leaves  will  diverge  farther, 
but,  if  negative,  they  will 
collapse.  FIG.  195. 

366.  Electrified  bodies  influence  bodies  at  a  distance 
in  a  manner  similar  to  the  action  of  a  magnet  on  magnetic 
substances.  This  influence  is  called  electrical  induction;  and 
the  resulting  effect,  induced  electricity. 

A.  Jfl  B 


FIG.  196. 


Let  A  B  be  a  conductor  of  brass,  insulated  on  a  glass  pillar 
and  furnished  with  a  number  of  pith  ball  electroscopes. 
If  this  is  brought  near  an  electrified  body,  C,  but  not  so 


INDUCTION.  237 

near  as  to  receive  a  spark  from  it,  the  balls  will  diverge  as 
shown  in  Fig.  196.  By  means  of  the  gold-leaf  electroscope 
we  may  ascertain  that  the  nearer  end,  A,  of  the  conductor 
contains  electricity  opposite  to  that  of  the  electrified  body, 
C,  and  the  further  end,  B,  the  same  kind.  If  C  be  posi- 
tively charged,  its  effect  will  be  to  repel  the  positive  elec- 
tricity toward  the  end,  B,  and  to  attract  negative  electricity 
to  the  end,  A. 

367.  The  two  electrical  forces  may  be  separated  by  in- 
duction. Suppose  the  conductor,  AB,  to  be  made  of  three 
parts,  each  insulated  and  movable,  and  while  the  whole  is 
under  the  influence  of  a  positively  electrified  body,  let  the 
central  portion  be  removed.  (1)  This  part  will  either  yield 
no  spark  or  a  very  feeble  positive  one.  (2)  The  portion,  B, 
may  be  discharged  by  bringing  the  hand  near  it,  yielding  a 
spark  of  positive  electricity.  Its  electricity  is,  therefore, 
free  to  diffuse  itself.  (3)  So  long  as  A  and  C  remain  near 
each  other  neither  will  be  completely  discharged  on  touch- 
ing it  separately,  because  their  mutual  attractions  tend  to 
retain  their  opposite  electricities.  Electrical  forces  in  this 
condition  are  said  to  be  bound  or  disguised.  If  the  two  are 
separated,  A  will  yield  negative  and  C  positive  electricity. 
If  communication  is  made  between  them,  both  will  be  dis- 
charged by  the  union  of  their  opposite, forces. 

If  the  cylinder,  AB,  while  near  the  positive  ball,  C,  be 
touched  by  the  hand,  the  pith  balls  at  A  will  diverge  fur- 
ther— those  at  B  will  collapse.  As  the  hand  and  body  are 
conductors,  the  positive  electricity  will  be  repelled  to  the 
earth.  The  negative  can  not  escape  being  bound  by  the 
attraction  of  the  positive  ball,  C.  On  the  contrary,  it  will 
increase,  because  the  inductive  force  of  C  was  previously 
opposed  by  the  positive  electricity  accumulated  in  the  end, 
B.  If  the  hand  be  first  removed  from  the  cylinder  and 


238 


ELEMENTS  OF  PHYSICS. 


ifieii  the  inducing  body,  the  cylinder  will  remain  negatively 
charged. 

Therefore,  a  body  may  be  charged  by  induction,  or  by 
conduction.  In  conduction  there  is  a  transfer  of  either 
force  from  an  electrified  body  to  another  body.  In  induc- 
tion there  is  no  transfer  of  force;  but  an  excited  body 
induces  both  kinds  of  electricity  in  an  insulated  body,  which 
remains  charged  with  the  opposite  electricity  if  uninsulated, 
for  a  time,  in  the  presence  of  the  excited  body. 

368.  The  electrophorus,  Fig.  197,  consists  (l)vof  a  cake 
of  resinous  matter,  R,  resting  on  a  conducting  plate  of  tin, 
and  (2)  a  movable  metallic 
cover,  T,  provided  with  an  in- 
sulating handle,  G.  If  the  re- 
sinous cake  be  beaten  with  cat's 
fur  it  becomes  charged  with  neg- 
ative electricity.  If,  now,  the 
cover  be  placed  on  the  cake, 
its  condition  is  that  of  an  insu- 
lated conductor  in  the  presence 
of  an  electrified  body.  Its  lower 
surface  becomes  positive  and  its  upper  negative  by  induc- 
tion. The  cake  does  not  discharge  itself  into  the  cover, 
because  (1)  of  the  inequalities  of  its  surface  and  (2)  because 
of  its  non-conducting  power. 

If  the  cover  be  uninsulated  for  a  moment  by  touching  it 
with  the  finger,  the  negative  force  passes  to  the  ground, 
while  the  positive  is  held  bound  by  the  negative  electricity 
of  the  resin.  Now,  if  the  finger  be  first  removed,  and  then 
the  cover  raised  by  its  insulating  handle,  G,  its  positive 
electricity  diffuses  itself  over  its  surface,  and  the  cover  will 
yield  a  positive  spark  when  it  is  brought  near  a  conductor. 

As  the  cake  acts  only  by  induction,  when  once  charged  it 


FIG.  197. 


INDUCTION.  239 

retains  its  electricity  for  a  long  time,  and  may  be  made  to 
induce  any  number  of  successive  charges  in  the  disk. 

369.  To  explain  the  action  of  induction  we  may  sup- 
pose that  whenever  a  body  is  electrified,  the  molecules  of 
the    surrounding   medium   become    polarized.      Thus,  if   C 
represent   a   charged   body,  the   adjacent   molecules  of  air, 
as  a,  b,  c,  d,  will  become  polar-       „     a    b     c    d 

ized.     Fig.  198.     The  mole-  £fe  ^§^m   fo    C. Wf\ 

cules  of  any  insulated  con-  ^^  O  d  O  O  ^^B^ 

ductor,  as  A  B,  within  their  FIG.  i9<s. 

influence  will  also  become  polarized ;  but  as  they  are  con- 
ductors they  \vill  discharge  their  electrical  forces  one  into 
the  other,  and  thereby  the  cylinder  itself  will  become  polar- 
ized, as  if  it  were  a  huge  molecule. 

370.  Induction  takes  place  in  most,  if  not  all,  elec- 
trical phenomena. 

I.  In  attraction.     The  pith  ball  of  the  electrical  pendulum 
is  first  polarized,  like  the  cylinder,  AB,  Fig.  198.     The  side 
next  the  excited  glass  rod  becomes  negative  by  induction, 
and  as  soon  as  the  attraction  of  the  opposite  electrical  forces 
becomes  greater  than  the  repulsion  of  the  positive  electric- 
ity on  the  further  side  of  the  ball,  the  ball  flies  to  the  rod. 

II.  In  charging.     In  Figs.  196,  198,  suppose  C  positively 
charged  to  be  brought  toward  AB.     The  polarization  of 
AB  will  rise  higher  and  higher  in  proportion  as  C  comes 
nearer.     When  C  is  near  enough,  A  B  will  become  charged 
with  positive  electricity  either  by  spark  or  by  contact.     The 
most  probable  explanation  of  this  is,  that  at  a  high  state  of 
polarization  the  adjoining  particles  discharge  their  electrical 
forces   into   each   other.     By  the   spark   or   by  contact,  an 
equal  amount  of  the  two  electricities  combine  and  become 
neutral,  and  the  cylinder  becomes  charged,  not  by  receiving 
more  positive  electricity,  but  by  discharging  its  negative. 


240 


ELEMENTS  OF  PHYSICS. 


III.  In  discharging.  If,  now,  the  hand  be  brought  near 
the  positively  charged  conductor,  the  electricity  of  the  hand 
is  polarized.  Its  positive  electricity  passes  to  the  ground, 
and  its  negative  to  the  fingers.  At  contact,  the  negative  of 
the  hand  and  the  positive  of  the  cylinder  combine,  and  the 
molecules  of  the  cylinder  become  neutral  or  unpolarized. 

371.  The  molecules  of  conductors  are  easily  polarized 
and  discharged:  the  molecules  of  insulators  require  a  greater 
force   to   effect  polarization  and  discharge.      Magnetic  and 
electrical  induction  are  similar.     The  induction  of  magnetism 
in  soft  iron  is  rapid  but  temporary;    that  of  steel  is  slower 
but  permanent.     In   magnetic  induction,  however,  the  two 
forces  can  not  be  separated.     In  electrical  induction,  a  body 
may  be  charged  positively  or  negatively;    but  this  can  be 
effected  and  maintained  only  when  it  is  surrounded  by  insu- 
lating molecules   in  which   the   opposite  force    is   induced. 
Hence,  the  two  forces  are  always  present,  and  electricity, 
like  magnetism,  is  a  polar  force. 

372.  Electricity  is  found  only  on  the  surface  of  an 
insulated  body.     Let  a  brass   ball  be  suspended  by  a  silk 


FIG.  199. 


thread  and  be  closely  covered  by  two  hemispheres  of  brass. 
Fig.  199.  Now,  if  a  charge  be  communicated  to  the  ap- 
paratus, and  then  the  hemispheres  be  withdrawn,  the  elec- 


ELECTRICAL  APPARATUS.  241 

tricity  will  be  found  only  on  the  hemispheres.  This  is  a 
consequence  of  the  repulsion  of  like  electricities.  Another 
result  is  that  the  charge  tends  to  escape  from  bodies ;  hence, 

373.  The  charge  will  be  distributed  uniformly  only 
on  spherical  surfaces.     On  cylindrical  surfaces,  the  charge 
will   be  accumulated  at  the    ends.     If  the  ends  are  mere 
points,  there  will  be  so  great  an  increase  of  electrical  inten- 
sity that  the  body  will  be  discharged  with  great  facility  and 
generally  without   the  passage  of  a  spark.     Hence,  if  we 
wish  to  avoid  this,  the  ends  of  cylinders  should  be  rounded, 
and  no  sharp  edges  nor  points,  should  be  attached  to   the 
apparatus. 

374.  The  terms  quantity  and  intensity  will  be  under- 
stood by  reference  to  the  similar  use  of  the  same  words  with 
respect  to  heat ;  thus,  the  heat  of  molten  iron  is  intense,  but 
a  hogshead  of  boiling  water  contains  a  greater  quantity  of 
heat  than  a  pound  of  molten  iron.     In  one  case,  each  par- 
ticle is  in  very  rapid  vibration :    in  the  other,  very  many 
particles  are  in  vibration,  and  the  sum  of  all  the  vibrations 
is  the   quantity.      Electrical  intensity  has  reference   to    the 
amount  of  force  lodged  in  each  particle.     Electrical  quantity 
has  reference  both  to  the  number  of  particles  affected  and  to 
the  force  lodged  in  each.     There  is  both  quantity  and  inten- 
sity in  every  electrified  body,  but  the  charge  may  be  char- 
acterized by  the  predominance  of  either  quality.     The  inten- 
sity is  measured  by  its  power  to  effect  discharge  through  bad 
conductors ;  thus,  a  long  spark  is  evidence  of  great  intensity. 
In  statical  electricity,  the  quantity  is  always  small,  though 
its  intensity  is  sometimes  enormous. 

ELECTRICAL  APPARATUS. 

375.  There    are    many    forms   of   electrical    machines. 
Fig.  200  represents  Winter's  plate  machine,  which  is  one  of 

PHYS.  21. 


242  ELEMENTS  OF  PHYSICS. 

the  best.  This  consists  of  a  circular  plate  of  glass,  mounted 
on  a  glass  axis  which  is  supported  by  two  posts  of  dry 
wood  and  made  to  revolve  by  a  winch.  Friction  is  applied 


R 


FIG.  200. 

to  the  glass  plate  by  two  rubbers,  R,  made  of  stuffed 
leather,  and  coated  with  an  amalgam  of  mercury,  tin,  and 
zinc.  The  rubbers  are  kept  in  place  by  clamps  attached  to 
an  insulated  brass  ball,  N,  called  the  negative  conductor. 
Attached  to  the  rubber  are  two  wings  of  silk,  S,  to  prevent 
the  electricity  from  escaping  into  the  air. 

The  plate  also  passes  between  two  wooden  rings,  W,  which 
are  attached  to  an  insulated  brass  ball,  P,  known  as  the 
prime  conductor.  On  the  side  of  the  wooden  rings,  next  to 
the  glass  plate,  are  two  rows  of  brass  points,  which  are  con- 
nected by  tin  strips  to  the  prime  conductor. 

On  turning  the  plate,  the  friction  of  the  rubbers  develops 
both  electricities  — the  negative  on  the  rubbers,  the  positive 
on  the  glass.  The  negative  electricity  passes  to  the  nega- 


WINTER'S  MACHINE.  243 

tive  conductor.  The  positive  electricity  is  carried  on  the 
glass  between  the  wooden  rings,  and  here  acts  by  induction 
on  the  prime  conductor,  attracting  its  negative  electricity. 
This  negative  electricity  collects  on  the  points  inside  of  the 
rings,  W,  and  finally  attains  sufficient  intensity  to  pass 
through  the  intervening  air  and  unite  with  the  positive 
electricity  on  the  glass.  The  glass  plate  thereby  becomes 
neutral  as  at  first.  The  prime  conductor,  having  given  off 
its  negative  electricity  in  the  manner  described  on  page 
239,  remains  charged  with  positive  electricity. 

376.  If  both  conductors  were  insulated,  this  action 
would  soon  eeage,  because  the  positive  electricity  of  the 
prime  conductor  would  act  inductively  on  the  negative  of 
the  other  conductor,  and  thus  only  a  feeble  charge  would  be 
possible.  If  either  conductor  be  uninsulated,  its  electric 
intensity  will  become  zero,  and  thereby  leave  the  electric 
force  on  the  other  conductor  free.  Hence,  (1)  when  the 
rubbers  are  connected  by  a  brass  chain  to  the  ground,  posi- 
tive electricity  accumulates  on  the  prime  conductor.  (2) 
When  the  brass  chain  connects  the  prime  conductor  to  the 
ground,  negative  electricity  accumulates  on  the  negative 
conductor.  If  the  hand  is  brought  near  either  conductor, 
when  charged,  it  is  discharged  by  a  spark. 

The  length  of  the  spark  is  wonderfully  increased  by  the 
addition  of  a  large  wooden  ring,  I.  An  iron  wire  forms 
the  core  of  this  ring,  and  is  connected  with  the  prime  con- 
ductor. Without  the  ring,  which  may  be  removed  at  the 
pleasure  of  the  operator,  the  machine  will  give  a  spark  two 
inches  in  length ;  with  the  ring,  sparks  may  be  obtained  six 
or  seven  times  as  long,  but  proportionally  less  frequent. 
The  quantity  of  electricity  is,  in  both  cases,  the  same,  the 
ring  acting  only  by  induction,  and  preventing  discharge 
until  electricity  of  high  tension  is  attained. 


244  ELEMENTS  OF  PHYSICS. 

There  are  several  varieties  of  the  frictional  machine,  some 
with  plates,  others  with  cylinders,  but  the  action  of  all  is 
the  same. 

377.  There  are  other  machines  which  act  only  by  the 
induction  of  a  charged  surface.     Among  these  are  the  elec- 
trophorus,  and  Holtz's  machine,  which  may  be  briefly  char- 
acterized as  a  revolving  electrophorus. 

378.  There  is  a  limit  to  the  accumulation  of  electricity 
on  any  surface.     But,  if  two  conducting  surfaces  are  separ- 
ated by  an  insulating  medium,   the  intensity  will    be    in- 
creased by  the  mutual  inducing  action  of  the  two  surfaces. 
Any  arrangement  of  this  sort  is  said  to  act  as  a  condenser. 

379.  The  Leyden  jar  is  the  most  convenient  form  of  the 
condenser.     This  consists  of  a  glass  bottle,  coated  both  on 
the  inner  and  outer  surface  with   tin-foil  to  within   three 
inches  of  the  neck.      The  mouth  is  closed  with  a  plug  of 
varnished   wood,  through  which   passes   a    brass  wire    sur- 
mounted by  a  knob  and 

reaching    to    the    inner 

coating.     If  the  jar  be 

held  near  a  machine  in 

action,  sparks  will  pass 

to   the   interior   of   the 

jar,    but    after    awhile 

this  will  cease,  and  the 

jar  is  then  said  to   be  FIG.  201. 

charged.     Fig.  201. 

To  discharge  the  jar,  the  inner  and  outer  coatings  must 
be  brought  in  connection.  This  may  be  done  by  placing 
one  hand  on  the  outer  coating  and  bringing  the  other  hand 
near  the  knob.  A  brilliant  spark  will  then  pass  from  the 
knob,  and  the  experimenter  receives  a  peculiar  twitching 


THE  LEYDEN  JAE. 


245 


FIG.  203. 


sensation  called  the  electric  slwck.  The  discharge  may  also 
be  effected  by  means  of  a  discharging  rod,  which  consists 
of  a  jointed  wire  terminating  in  brass  knobs.  See  J  in 
Fig.  213. 

If  the  outer  coating  be  insulated,  the  jar  will  receive  little 
or  no  charge.  But  if  the  finger  be  then  brought  near  the 
outer  coating,  for  every  positive  spark  that  passes  into  the 
jar,  an  equal  spark  of  the  same  kind  will  pass  from  the 
outer  coating  to  the  finger. 

380.  The  action  of  the  jar  may  be  explained  as  follows: 
When  the  positive  spark  I  o  I  o 

passes  to  the  interior  of 
the  jar,  the  molecules  of  + 
the  glass  become  polar- 
ized, as  shown  in  Fig. 
202.  If  the  jar  be  in-  FIG.  202. 
sulated,  but  little  charge  can  be  received  because  of  the 
repulsion  of  the  positive  electricity  which  accumulates  on 
the  outer  surface.  If,  now,  the  outer  coating  be  connected 
with  the  ground,  the  positive  electricity  escapes  from  it, 
and,  consequently,  the  outer  layer  becomes  charged  with 
negative  electricity,  as  represented  in  Fig.  203. 

The  outer  surface  is,  therefore,  charged  by  induction. 
The  two  surfaces  have  very  nearly  equal  charges  of  opposite 
electricities  which  are  held  mutually  bound,  so  that  neither 
can  be  discharged  separately.  The  amount  of  charge  which 
a  jar  may  receive  is  in  proportion  to  the  facility  it  offers  for 
induction.  The  thinner  the  glass,  the  better ;  but  if  too 
thin,  the  polarization  may  rise  high  enough  to  cause  a  dis- 
charge through  the  glass,  thereby  perforating  it. 

The  charge  is,  therefore,  dependent  rather  on  the  glass 
than  on  the  coatings.  This  is  shown  by  means  of  a  jar 
with  movable  coatings.  (Fig.  204.)  If  the  parts  be  put  in 


246 


ELEMENTS  OF  PHYSICS. 


place  and  the  jar  charged,  the  coatings  may  be  removed 
and  discharged.  On  again  replacing  the  parts,  a  charge 
may  be  received  almost  as  strong  as  if  the 
coatings  had  not  been  removed.  Hence, 
the  principal  office  of  the  coatings  is  that 
of  a  conductor,  to  connect  the  polarized 
molecules  of  the  glass.  Another  evidence 
of  this  is  that  the  glass  cup,  .B,  may  be 
charged  separately  by  rotating  its  inner 
surface  on  the  knob  of  the  prime  con- 
ductor, and,  then,  if  the  two  coatings  are 
applied,  the  whole  combination  will  be  dis- 
charged by -a  single  spark. 

381.  If  a  series  of  jars  be  insulated 
except  the  last,  as  in  Fig.  205,  all  may  be 
charged  simultaneously.  The  electricity 
repelled  from  the  first,  charges  the  second, 
and  so  on.  Each  may  then  be  discharged  separately.  Or 
all  the  similar  coatings  may  be  connected  to  form  an  elec- 


FlG.  204. 


FlG.  205. 

tried  battery,  as  represented  in  Fig.  213,  and  discharged  by 
a  single  spark. 


ELECTRICAL  PHENOMENA. 

382.   The  laws  and  phenomena  of  electricity  may  be 
illustrated  by  a  great  number  of  experiments. 


ELECTRICAL  PHENOMENA. 


247 


1.  Repulsion.     If  a  person  stands  on  a  stool  supported  by 
glass  legs  and  touches  the  prime  conductor,  he  becomes,  in 
fact,  a  part  of  it ;  and  sparks  may  be  drawn  from  him  with 
the  same  effect  as  from  the  cylinder.     His  hair,  if  dry  and 
loose,  will  stand  out  in  a  fantastic  manner,  because  the  sep- 
arate hairs  are  charged  with  the  same  electrical  force. 

2.  Attraction.     If,  now,  a  bystander  bring  his  hand  over 
the    electrified    person,  the  hairs  will   converge   toward   it. 
Negative  electricity  is  induced  in    the  hand,  and  the  two 
bodies  oppositely  electrified  attract  each  other. 

3.  Attraction   and  repulsion.      The  electrical  chimes,  Fig. 
206,  consist  of  two  bells  in    metallic   connection  with   the 
machine,  and  of  a  third  bell,  insulated  by 

a  silk  thread  from  the  machine,  but  con- 
nected with  the  ground.  Between  the 
bells  are  small  brass  balls  suspended  by 
silk  threads.  On  work- 
ing the  machine,  the 
outer  bells  are  posi- 
tively electrified,  and  in- 
duce negative  electricity 
in  the  middle  bell.  The 
balls  are  alternately  at- 
tracted and  repelled  by 
the  outer  and  inner  bells,  and  thus  a 
constant  ringing  is  kept  up. 

The  electrical  hail  is  exhibited  by  means 
of  two  metal  plates,  one  connected  with 
the  ground   and  the   other  with  the   ma- 
chine, as  in  Fig.  207.      Light  pith  balls 
FIG.  207.  or  grotesque  figures  placed   between    the 

plates  when  the  machine  is  in  action  rise  and  fall  in  an 
irregular  manner. 


FlG.  206. 


248 


ELEMENTS  OF  PHYSICS. 


383.  The    kinds    of   electrical   discharge    are    three: 
(1)  conductive,  as  when  the  electricity  passes  through  a  good 
conductor  without  light ;  (2)    disruptive,  as  effected  through 
a  bad   conductor   and    attended  with  light ;    (3)   convective, 
which  is  effected  by  particles  of  matter  passing  away  from 
a  charged  surface. 

The  electrical  hail  is  an  example  of 
convective  discharge,  but  usually  it  is 
effected  by  the  movements  of  parti- 
cles  of  air  passing  away  from  a  point 
on  a  charged  surface.  Quite  a  cur- 
rent of  air  may  be  detected  by  per- 
sons standing  near  such  a  point. 
The  face  feels  as  if  a  cobweb  were 
drawn  over  it.  The  electric  whirl 
consists  of  a  number  of  such  points 
suspended  on  a  pivot.  Fig.  208.  FIG.  208. 

The  reaction  of  the  current  of  air  is  sufficient  to  turn  the 
wheel  rapidly  about. 

384.  Flames  act  as  points.     If  a  candle  be  held  near 
a  charged  conductor,  the  flame  will  be  repelled,  as  shown 

in  Fig.  209,  and  sometimes 
extinguished.  If  the  can- 
dle be  placed  on  the  con- 
ductor and  a  point  turned 
toward  it,  the  flame  will 
be  driven  in  the  con- 
trary direction.  This  is 
due  to  the  current  of  air 
which  sets  out  from  the 
point  which  has  become 
negatively  electrified  by  induction. 

385.  Luminous  effects.    If  a  discharge  be  passed  through 


LUMINOUS  EFFECTS. 


249 


an  interrupted  conductor,  a  succession  x>f  sparks  Avill  be  ob- 
tained, which,  when  exhibited  in  a  darkened  room,  yield  a 
brilliant  display.  The  luminous  tube  may  be  used  for  this 

purpose.     Fig.  210.     It  con- 

sists of  a  glass  tube  on  which 

are  pasted  in  a  spiral  form 

bits  of  tin-foil. 
When  the  discharge  passes 

off  from  the  thin  edge  of  a 

plate,   a   number    of   feeble 

sparks    are   obtained,  which 

assume  the  form  of  a  brush. 
If  the  discharge  is  effected 

in  rarefied  gases  the  effect  is 

very  beautiful.     For  this  ex- 

periment a  receiver  called  the 

aurora   tube  is  used.      Fig. 

211.      In    rarefied    air    the 

light  has  a  bluish  color;   in 

nitrogen,  more  of  a  purple; 
FIG.  210.      in  hydrogen,  a  fine  crimson. 

386.  The  duration  of  the  spark  is  less  than  one  -mil- 
lionth part  of  a  second.  If  Newton's  wheel,  Fig.  166,  be 
set  in  very  rapid  rotation  in  a  dark  room  and  be  illumi- 
nated by  an  electric  spark,  the  wheel  will  appear  stationary. 
387.  The  velocity  of  the  discharge  in  copper  wire  is 
estimated  at  288,000  miles  in  a  second.  This  was  measured 
by  transmitting  the  discharge  of  a  Leyden  jar  through  a 
very  long  copper  wire.  The  circuit  was  broken  at  three 
points,  one  at  the  middle  of  the  wire  and  one  near  each 
coating.  In  this  way  three  sparks  were  formed,  which,  to 
the  eye,  seemed  instantaneous.  When  they  were  viewed  by 
means  of  a  revolving  mirror,  they  presented  the  appearance 


2ii. 


250  ELEMENTS  OF  PHYSICS. 

of  three  arcs  of  equal  length,  the  middle  one  rather  behind 
the  others,  as  in  Fig.  212.     The  velocity  with  which  the 
mirror  revolved  was  known,  and  from  this  the  retardation 
was  calculated  which  gave  the  velocity  of  trans- 
mission.     The  velocity  is    found    to   vary  both 
with  the  nature  of  the  conducting  medium  and 
the  intensity  of  the  charge. 

388.  Calorific  effects.  Any  combustible  substance,  as 
ether,  is  readily  inflamed  by  the  spark.  Very  thin  wires 
may  be  melted  by  a  discharge  from  a  Leyden  battery.  Fig. 
213.  Those  wires  are  heated  most,  which  are  the  worst 
conductors.  In  using  this  battery  the  apparatus,  U,  on  the 


FIG.  213. 

right  of  the  figure,  is  convenient.  It  consists  of  three  glass 
posts,  two  of  which  carry  jointed  rods,  while  the  center 
bears  on  its  top  a  glass  plate.  A  thin  gold  wire,  a  b,  sup- 
ported on  this  by  a  paper  card,  c,  is  instantly  volatilized  by 
a  powerful  discharge. 

Chemical  effects.  The  peculiar  odor  which  always  accom- 
panies the  electrical  discharge  is  due  to  the  formation  of 
ozone,  an  allotropic  modification  of  the  oxygen  of  the  air. 


ATMOSPHERIC  ELECTRICITY.  251 

A  succession  of  sparks  passed  through  ammonia  decomposes 
it.  The  spark  may  also  effect  chemical  combination. 

Thus,  if  two  volumes  of  hydrogen  and  one  of  oxygen  be 
mixed  in  the  electrical  pistol,  Fig.  214,  a 
single  spark  will   cause  them   to  combine 
with  a  loud  explosion. 

389.  The  mechanical  effects  are  shown 
when   a  discharge    passes   through  a  poor 
conductor.    If  a  discharge  is  passed  through 
a  card  of  thick  paper,  a  burr  will  be  pro- 
duced in  both   directions.     A  glass  plate 

maybe  perforated  by  a  moderately  strong  FIG.  214.    ^ 

charge.  The  mechanical  effects  of  lightning  are  well  known. 
It  rends  and  tears  every  obstacle  which  hinders  its  free 
transmission,  with  amazing  force.  The  noise  which  accom- 
panies the  spark  is  due  to  the  sudden  expansion  of  the 
surrounding  air,  followed  by  a  sudden  collapse,  thereby  pro- 
ducing a  sonorous  wave  of  condensation  and  rarefaction. 

390.  Physiological  effects.     Quite  a  number  of  persons 
may  receive  the    electric   spark   simultaneously.     For  this 
purpose,  all  must  join  hands,  the  first  touching  the  knob  of 
a  Leyden  jar,  and  the  last  the  outside. 

Electricity  has  also  been  found  of  service  in  the  treatment 
of  some  diseases.  For  this  purpose,  as  well  as  for  producing 
chemical  decomposition  and  magnetic  effects,  which  require 
quantity  rather  than  intensity,  some  form  of  dynamical  elec- 
tricity is  generally  employed. 

ATMOSPHERIC   ELECTRICITY. 

Franklin  demonstrated,  in  1752,  that  a  flash  of  lightning 
is  simply  an  enormous  spark  of  electricity.  He  raised  a  silk 
kite  at  the  approach  of  a  storm,  and  as  soon  as  the  rain 
had  wetted  his  hempen  kite  string,  thereby  rendering  it  a 


252  ELEMENTS  OF  PHYSICS. 

good  conductor,   he    succeeded    in   drawing  sparks  from  a 
key  hung  on  the  string  and  in  charging  a  Leyden  jar. 

391.  The  principal  source  of  atmospheric  electricity  is 
supposed  to  be  the  evaporation  and  subsequent  condensation 
of  water.     A  cloud  becomes   positively   electrified   by   the 
accumulation  of  the  electricity  which,  before  its  formation, 
was  disseminated  through  its  particles.     It  is  probable  that 
negative  clouds  are  mostly  due  to  the  inductive  action  of 
other  positively  charged  clouds. 

The  earth  beneath  a  cloud  is  subject  to  the  same  inductive 
action  and  becomes,  by  consequence,  charged  with  electric- 
ity opposite  to  that  of  the  cloud. 

392.  A  flash   of  lightning   is  produced  when  the  air 
between   two   adjacent    bodies  oppositely  charged    becomes 
highly  polarized.     The  light  is  due  to   the  intense  heat  of 
the  discharge  which  renders  the  particles  of  the  air  incan- 
descent.    The  thunder  is  due  to  the  violent  commotion  pro- 
duced in  the  air  by  its  sudden  expansion  along  the  path  of 
the  flash,  and  is  prolonged  by  echoes. 

Heat  lightning  is  the  name  applied  to  bright  flashes  of 
light  observed  in  the  horizon  on  summer  evenings.  This  is 
generally  due  to  the  reflection  by  the  atmosphere  of  ordi- 
nary lightning  so  distant  that  the  thunder  is  inaudible. 

393.  Lightning  conductors  are   metallic  rods  used  to 
protect  buildings  from  the  effects  of  lightning.     (1.)    They 
offer  to  the  discharge  the  line  of  smallest  resistance.     Hence, 
the  rod  should  be  a  good  conductor,  continuous  from  top  to 
bottom,  and  should  terminate  in  earth  which  is  permanently 
moist.      (2.)    They  may  prevent  the  discharge.     If  the  rods 
are  tipped  with  points,  the  discharge  may  be  effected  silently 
and   the   polarization   of  the  air  particles  never  rise  high 
enough  to  produce  the  flash. 


AURORA  BOREALIS.  253 

394.  There  are  other  phenomena  of  atmospheric  elec- 
tricity among  which  may  be  mentioned  the  Aurora  Borealis, 
or  northern  lights,  and  St.  Elmo's  fire.  It  has  been  noticed 
that  during  the  auroras  the  telegraph  lines  have  been  dis- 
turbed so  as  to  prevent  sending  intelligible  dispatches,  and, 
also,  that  telegraphs  may  be  worked  without  the  aid  of  a 
battery  when  the  auroras  are  very  bright,  as  was  the  case 
in  1869. 

KECAPITULATION. 

I.   The  phenomena  of  statical  electricity  are : 
By  friction. 


1.  Excitation        , 

By  other  molecular  disturbances. 

2.  Attraction  of  bodies  charged  with  unlike  electricities. 

3.  Repulsion  of  bodies  charged  with  like  electricities. 

f    On  the  surface  of  insulated  conductors. 

4.  Distribution      4 

(    Accumulated  at  pointed  extremities. 


f   Readily  in  conductors. 
By  conduction     •< 


Slowly  in  insulators. 

5.  Transference   (    By  convection  in  moving  particles. 

f   Spark. 
By  Eruption      (   ^^ 

6.  Induction  .     .     By  a  charged  body  on  insulating  matter. 

II.  The  effects  of  statical  electricity  are  : 

1.  Mechanical    .      By  producing  fracture. 

2.  Luminous       .      In  the  electric  spark. 

3.  Calorific     .    .      By  evolving  heat. 

f   By  effecting  combination. 

4.  Chemical   .      ]    . 

(    By  decomposing  compounds. 

5.  Physiological  .    In  producing  electric  shocks. 


254  ELEMENTS  OF  PHYSICS. 


DYNAMICAL  ELECTRICITY. 

395.  All  chemical  actions  are  attended  with  the  devel- 
opment of  electrical  force.  This  force  is  identical  with  that 
produced  by  friction  ;  but  because  its  discharge  is  continu- 
ous that  department  of  electrical  science  which  treats  of 
electricity  produced  by  chemical  action  is  called  dynamical 
electricity.  It  is  also  called  Galvanism  and  Voltaic  electricity 
in  honor  of  Galvani  and  Volta,  who  were  among  the  first 
to  study  its  phenomena. 

The  fundamental  phenomena  of  dynamical  electricity  may 
be  exhibited  by  means  of  the  simple 
Voltaic  element.  Fig.  215.  This  usu- 
ally  consists  of  a  glass  vessel  contain- 
ing a  plate  of  amalgamated  *  zinc  and 
a  plate  of  copper,  partially  immersed 
in  water  to  which  a  little  sulphuric 
acid  has  been  added.  A  chemical 
action  takes  place,  by  which  (1)  the 
water  is  decomposed  ;  its  hydrogen  is  FIG.  215. 

liberated  and  its  oxygen  combines  with  the  zinc  to  form 
zinc  oxide.  With  water  alone  this  action  is  very  feeble, 
because  the  zinc  oxide  soon  forms  a  coating  on  the  zinc 
plate,  which  does  not  dissolve  in  water.  (2)  The  sulphuric 
acid  prevents  the  formation  of  this  coating.  This  it  does 
by  uniting  with  the  oxide  to  form  zinc  sulphate,  which 
readily  dissolves  in  the  liquid  and  leaves  the  plate  clean. 
The  copper  is  not  chemically  acted  upon  and  serves  merely 
as  a  conductor  of  the  electricity. 


*To  amalgamate  zinc,  it  is  first  cleaned  -by  immersion  in  dilute 
sulphuric  acid  and  then  mercury  is  rubbed  over  its  surface. 


ELECTRICAL   CIRCUIT.  255 

As  soon  as  the  plates  are  immersed,  there  is  a  slight  dis- 
engagement of  hydrogen  and  both  plates  become  feebly 
charged  with  electricity.  If  the  plates  are  kept  from 
touching,  no  further  action  will  be  perceived.  The  whole 
arrangement  is  in  a  polarized  condition,  which  may  be  re- 
presented by  Fig.  216,  in  which  the  positive  molecules  are 
shaded.  The  outer  end  of  the  zinc  is  nega- 
tive, and  the  portion  in  contact  with  the  liquid 
is  positive.  The  negative  molecules  of  the 
liquid  are  turned  toward  the  zinc  and  the  pos- 
itive toward  the  copper  plate.  The  copper 
thus  becomes  polarized  in  a  sense  opposite  to  that  of  the 
zinc. 

If,  now,  the  plates  are  brought  in  contact  either  directly 
or  by  means  of  a  metallic  wire,  a  discharge  will  take  place 
through  the  whole  combination  or  circuit.  At  the  same  time, 
the  chemical  action  increases  and  gives  rise  to  a  series  of 
charges  and  discharges  in  such  rapid  succession,  that  the  dis- 
charge appears  continuous  and  the  circuit  is  said  to  be  trav- 
ersed by  an  electrical  current.  The  current  continues  so  long 
as  the  contact  is  maintained,  but  ceases  wThen  the  plates  are 
disconnected.  The  operation  of  connecting  the  plates  is 
called  closing  the  circuit,  and  the  separating  of  them  is  called 
breaking  the  circuit. 

396.  It  is  to  be  noted  that  when  the  circuit  is  closed, 
the  hydrogen  rises  only  from  the  surface  of  the  copper.  In 
explanation  of  this,  it  is  supposed  that  when  the  oxygen 
and  zinc  combine,  a  molecule  of  hydrogen  is  set  free,  and 
unites  with  the  oppositely  electrified  oxygen  in  the  neigh- 
boring molecule  of  water,  and  displaces  its  hydrogen.  This 
molecule  of  hydrogen  is  transferred  to  the  adjacent  molecule 
of  water,  and,  in  like  manner,  the  same  transference  takes 
place  throughout  the  whole  series  until  the  hydrogen  of  the 


256  ELEMENTS  OF  PHYSICS. 

molecule  of  water  next  to  the  copper  is  displaced.  This 
hydrogen  can  not  combine  with  the  copper,  but  discharges 
its  free  positive  electricity  into  it  and  escapes  in  a  gaseous 
state. 

Each  successive  transfer  of  the  hydrogen  may  be  assumed 
to  be  accompanied  by  a  separation  and  recombination  of  the 
opposite  electricities.  The  current  itself  must  be  considered 
as  due  to  a  constant  series  of  polarization  and  discharge 
among  all  the  molecules  of  the  Voltaic  element,  both  liquid 
and  solid,  by  reason  of  which  there  is  a  transmission  of  both 
electrical  forces  throughout  the  circuit,  the  positive  going 
one  way  and  the  negative  the  other. 

To  avoid  confusion,  only  the  direction  of  the  positive  cur- 
rent is  usually  given  in  speaking  of  the  current.  The  direc- 
tion of  the  positive  current  (1)  within  the  liquid  is  from 
the  zinc  to  the  copper,  and  (2)  without  the  liquid,  from  the 
copper  to  the  zinc. 

397.  The  current  always  sets  out  from  the  metal  most 
easily  acted  upon  by  the  liquid,  which  is  therefore  called 
the  generating  or  positive  plate.  The  other  metal  is  called  the 
conducting  or  negative  plate.  In  most  Voltaic  elements,  the 
liquid  used  is  dilute  sulphuric  acid;  that  is,  acid  to  which 
has  been  added  from  ten  to  twenty  times  its  bulk  of  water. 
The  electric  deportment  of  several  substances  with  reference 
to  this  acid  is  given  in  the  following  Electro-motive  series: 

-j-Zinc.  Lead.  Iron.  Nickel.  Bismuth.  Antimony. 
Copper.  Silver.  Platinum  — . 

In  this  list,  the  metals  named  are  positive  with  reference 
to  those  that  follow  them,  and  are  negative  with  reference 
to  those  that  precede. 

Poles.  The  current  passes  without  the  liquid,  from  the 
negative  plate  back  to  the  positive  plate ;  hence,  if  the  con- 
necting wire  be  cut,  the  positive  electricity  will  tend  to 


ELECTRO -MOTIVE  FORCE.  257 

accumulate  at  the  end  of  the  wire  attached  to  the  negative 
or  copper  plate  and  the  negative  electricity  to  the  positive 
or  zinc  plate.  These  ends  are  called  the  poles  or  electrodes 
t)f  the  circuit.  In  most  combinations,  zinc  is  used  for  the 
positive  plate ;  the  wire  attached  to  it  is  called  the  negative 
pole  or  electrode.  The  wire  attached  to  the  negative  plate 
is  the  positive  electrode  or  pole. 

398.  The  electro-motive  force,  or  that  which  causes  or 
tends  to  cause  a  transfer  of  electricity,  is  dependent  on  the 
relation  which  the  metals  bear  to  the  liquid.     It  is  greater 
the  farther  apart  the  metals  are  in  the  series.     Dilute  sul- 
phuric acid  acts,  upon  copper  when  taken  by  itself;  hence, 
it  tends  to  produce  on  'the  copper  plate  a  current  acting  con- 
trary to  that  developed    on  the  zinc.     The  electro-motive 
force  of  the  Voltaic  element  is,  therefore,  due  to  the  differ- 
ence of  these  two  opposing  forces.     Now,  as  dilute  sulphuric 
acid  does  not  act  upon  platinum  at  all,  a  stronger  current 
may  be  established  between  zinc  and  platinum  than  between 
any  other  two  metals  in  the  series. 

399.  The  quantity  of  electricity  produced  by  a  Voltaic 
element  is  proportional  to  the  chemical  activity.     The  work 
which  the   current  can  do  is,  therefore,  proportional  to  the 
amount  of  zinc  consumed  in  a  given  time.     The  quantity  is 
at  all  times  enormous.     It  has  been  calculated  that  an   ele- 
ment which  might  be  contained  in  a  lady's  thimble  is  capa- 
ble of  evolving  a  greater  quantity  of  electricity  than   the 
largest  electrical  machine  ever  constructed. 

400.  The  intensity  of  the  current  depends  both  on  the 
electro-motive  force  and  the  resistance  which  is  to  be  over- 
come.    The  greater  the  electro-motive  force,  the  greater  will 
be  the  intensity ;    the  greater  the  resistance,  the  less  will  be 
the  intensity.     This  relation,  then,   may   be   expressed   by 
Ohm's  law : 

PHYS.  22. 


258  ELEMENTS  OF  PHYSICS. 

Electro-motive  force 


Intensity  of  current  = 


resistance. 


401.  The  resistance  is  inversely  as  the  conducting  power 
of  the  substance  through  which  the  current  passes.     The 
conducting  power  of  different  substances  of  equal  dimensions 
is  shown  relatively  by  the  following  table: 

Solids.  Liquids. 

Silver          .        .  100.  Mercury 1.6 

Copper       .        .  99.9  Dilute  sulphuric  acid         .        .      .00009907 

Zinc    ...        29.  Strong  nitric  acid        .        .        .      .00008808 

Platinum  .        .        18.  Common  salt,  saturated  solution     .00003152 

Iron    .        .        .         16.8  Sulphate  of  copper "  "  .00000542 

Carbon       .        .  .04  Distilled  water 00000001 

It  is  manifest  that  the  resistance  will  increase  with  the 
lepgth  of  the  conductor,  and  also  that  it  will  decrease  as 
{he  area  of  its  cross  section  increases.  Hence,  the  shorter 
and  thicker  the  connecting  wire,  the  less  will  be  the  resist- 
ance. So,  also,  the  nearer  the  plates  are  together  and  the 
larger  their  area,  the  less  will  be  the  resistance  offered  to 
the  current  by  the  liquid  layer  between  them. 

The  table  shows  that  the  resistances  offered  by  liquids  are 
enormous  when  compared  with  solids.  Hence,  the  resistance 
caused  by  the  liquid  between  the  plates  is  far  greater  than 
in  a  short  conducting  wire.  When  the  conducting  wires 
are  very  long,  as  in  telegraphs,  the  external  resistance  may 
exceed  the  internal. 

402.  A  Voltaic  Battery  consists  of  several  Voltaic  ele- 


n  tyt 


FIG.  217. 

ments  so  connected  that  the  current  has  the  same  direction 
in   all.     The   efficiency  of  the  battery  will   vary  with  the 


VOLTAIC  CIRCUIT.  259 

manner  of  grouping  the  elements.  For  the  sake  of  illus- 
tration, take  six  elements,  each  containing  a  square  inch  of 
zinc,  separated  from  a  copper  plate  by  a  liquid  layer  an 
inch  in  thickness.  If  all  the  similar  plates  are  connected, 
as  represented  in  Fig.  217,  the  effect  will  be  the  same  as 
that  of  a  single  element  having  a  zinc  plate  of  six  square 
inches,  one  inch  .distant  from  the  copper  plate.  Either 
arrangement  is  called  a  simple  Voltaic  circuit. 

In  the  compound  Voltaic  circuit  the  positive  plate  of  each 


FIG. 218. 

element  is  connected  with  the  negative  plate  of  the  adjoin- 
ing element,  as  shown  in  Fig.  218. 

The  simple  circuit  is  sometimes  called  a  quantity  battery. 
It  is  used  when  the  external  resistance  is  very  small.  It  is 
adapted  for  producing  thermal  effects,  such  as  melting  wires. 
The  compound  circuit  is  sometimes  called  an  intensity  bat- 
tery. It  is  used  when  the  external  resistance  is  very  great. 
It  is  adapted  for  telegraphs,  for  the  electric  light,  and  for 
producing  chemical  decomposition. 

403.  Numerous  batteries  have  been  constructed  on  the 
principle  of  the  Voltaic  element  already  described,  but  most 
of  them  have  gone  out  of  use,  because  of  the  rapid  enfee- 
blement  of  the  current. 

This  may  occur  (1)  from  the  gradual  consumption  of  the 
acid  and  the  zinc,  and  (2)  from  local  action.  By  local  action 
is  meant  the  production  of  small  closed  circuits  on  the  posi- 
tive plate,  which  are  due  to  impurities  on  the  zinc  plate. 
This  is  remedied  by  amalgamating  the  zinc.  (3)  Besides 
these  defects,  the  older  batteries  were  liable  to  what  is  called 
the  galvanic  polarization  of  the  plate.  In  the  action  of  the 


260 


ELEMENTS  OF  PHYSICS. 


simple  element,  the  hydrogen  is  apparently  evolved  from  the 
copper.  In  the  process  of  time,  the  copper  becomes  coated 
with  a  layer  of  positive  hydrogen,  which,  of  itself,  would 
weaken  the  current,  but  which  acts  the  more  injuriously 
because  it  reduces  the  zinc  sulphate,  and  thereby  forms  a 
layer  of  metallic  zinc  on  the  copper. 

4O4.  Constant  batteries  obviate  this  last  defect  by  pre- 
venting the  permanent  deposition  of  the  hydrogen  on  the  neg- 
ative plate.  There  are  over  fifty  forms  of  constant  batteries ; 
among  the  best  of  them  are  the  following  two-fluid  batteries : 

Grove's  battery  consists  of  (1)  a  glass  cup  containing 
a  hollow  cylindrical  zinc  plate  and  weak  sulphuric  acid; 
(2)  of  a  porous  cup  made  of  unglazed 
earthenware,  containing  strong  nitric  acid 
and  a  strip  of  platinum.  The  porous  cup 
and  its  contents  are  placed  inside  the 
zinc  cylinder.  Fig.  219. 

The  hydrogen  which  is  liberated  by 
the  action  of  the  zinc  passes  by  osmosis 
through  the  porous  cup,  and  on  meeting  FIG.  219. 

the  nitric  acid  unites  with  a  part  of  its  oxygen  to  form 
water,  and  reduces  the  acid  to  nitric  oxide.  This  oxide  is 
either  dissolved  in  the  liquid  or  escapes 
in  red  fumes. 

Bunsen's  battery  (Fig.  220)  is  sim- 
ply a  large  Grove's  battery  in  which 
the  platinum  slip  is  replaced  by  a  carbon 
cylinder.  The  chemical  action  is  the 
same  as  the  preceding,  but  as  the  ele- 
ments are  larger,  for  the  same  amount 
of  zinc  consumed,  Bunsen's  battery  gives 
a  greater  quantity  of  electricity,  but  less 
intensity,  than  Grove's. 


FIG.  220. 


CONSTANT  BATTERIES.  261 

In  this  form  the  nitric  acid  is  sometimes  advantageously 
replaced  by  a  mixture  of  one  part  of  potassium  bichromate, 
two  of  sulphuric  acid,  and  ten  of  water. 

DanieWs  battery  (Fig.  224)  may  readily  be  constructed 
by  the  student  by  placing  within  the  porous  cup  a  zinc 
plate  and  dilute  sulphuric  acid,  and  in  the  outer  vessel  a 
thin  roll  of  copper  with  a  saturated  solution  of  sulphate  of 
copper.  The  hydrogen,  liberated  by  the  action  of  the  zinc, 
enters  the  solution  of  the  sulphate  of  copper  and  reduces  it, 
forming  (1)  metallic  copper,  which  is  deposited  on  the  neg- 
ative plate;  and  (2)  sulphuric  acid,  which  passes  by  osmosis 
into  the  porous  cup,  and  replaces  the  acid  which  was 
neutralized  by  the  zinc. 

KECAPITULATION. 

I.  A  Voltaic  element  may  consist  of, 

1.  Two  metals  and  one  fluid    ....    Voltaic. 

T  Grove's. 

2.  Two  metals  and  two  fluids  .     .    .    4    Bunsen's. 

(.  Daniell's. 

II.  The  Voltaic  current  is  due, 

1.  To    the  polarization   of    the   metallic    and  liquid   particles, 
composing  the  circuit. 

2.  To  the  contact  of  two  dissimilar  metals. 
"3.   To  a  chemical  action  on  one  metal. 

4.   To  a  transfer  of  the  fluid  molecules. 

III.  The  Voltaic  current  depends, 

1.  On  the  electro-motive  force. 

2.  On  the  chemical  action. 

3.  On  the  resistance,  both  internal  and  external. 

IV.  The  Voltaic  circuit  may  be    .  j   Dimple. 

(    Compound. 


262 


ELEMENTS  OF  PHYSICS. 


THE  PHENOMENA  OF  DYNAMICAL  ELECTRICITY. 


405.  The  effects  of  the  current  are  manifested  either 
(1)  within  its  path,  or  (2)  external  to  its  path.  The  for- 
mer will  be  first  considered. 

Physiological  effects.  The  science  of  dynamical  electric- 
ity is  said  to  owe  its  origin  to  an  experiment  of  Galvani  in 
1790,  which  may  be  repeated  in  the  following  manner : 

Let  a  strip  of  2inc  be  passed  below  the  crural  nerve  of  a 
frog,  recently  killed,  and  a 
copper  wire  be  made  to 
touch  the  muscles  of  the 
legs,  as  shown  in  Fig.  221. 
Each  time  the  ends  of  the 
metals  are  brought  together 
at  A,  the  legs  are  thrown 
out  in  the  direction  of 
the  dotted  lines.  The  same 
convulsive  movements  take 
place  when  one  pole  of  a 
battery  touches  the  nerve 
and  the  other  the  muscles. 
The  muscles  contract  as  FIG.  221. 

often  as  the  circuit  is  opened  and  closed,  but  remain  quiet 
when  the  current  is  passing.  Hence,  the  more  frequently 
and  abruptly  the  circuit  is  broken  and  closed,  the  greater 
will  be  the  physiological  effect. 

If  the  electrodes  of  a  strong  compound  circuit  be  grasped 
with  the  hands,  previously  moistened,  a  shock  will  be  expe- 
rienced; but,  unless  the  number  of  elements  is  considerable, 
the  sensation  is  hardly  perceptible.  The  nerves  of  the  pal- 
ate and  of  sight  are  easily  affected.  If  a  strip  of  zinc  be 


EFFECTS  OF  THE  CURRENT. 


263 


placed  above  the  tongue  and  a  strip  of  silver  between  the 
gums  and  the  cheek,  as  often  as  the  metals  are  made  to 
touch,  a  peculiar  taste  will  be  experienced,  and  a  flash  of 
light  will  seem  to  pass  before  the  eye. 

406.  Calorific  effects.     If  a  current  be  passed   through  a 
thin  metallic  wire,  the  wire  will  be  heated  in  proportion  to- 
the  quantity  of  electricity  and  the  resistance  offered  by  the 
wire.      The  wire  may   become  incandescent,   may   fuse,  or 
even  be  dissipated  in  vapor.     With  the  same  current,  the 
worst  conductors  will  be  the  most  readily  heated.     Thus,  if 
a  suitable  current  be  passed  through  a  chain  made  of  alter- 
nate links  of  platinum  and  silver,  it  may 

render   the    platinum   incandescent,  while 
the  silver  remains  dark. 

On  the  same  principle,  if  a  platinum 
wire  be  interposed  in  any  part  of  the  cir- 
cuit, it  may  be  made  to  ignite  gunpowder. 
This  has  been  turned  to  account  in  blast- 
ing rocks  and  exploding  torpedoes. 

407.  Luminous  effects.     No  spark  is  ob- 
tained unless  the  poles  are  brought  in  con- 
tact,  or   nearly  so.      With   a   moderately 
strong  battery,  sparks  may  be  obtained  at 
the    moment   the    circuit    is    broken    and 
closed.      A  most  brilliant  electric  light  is 
obtained  by  connecting  the  terminal  wires 

with  carbon  points,  as  shown  in  Fig.  222.  The  carbon  points 
are  first  brought  in  contact,  and  the  heat  developed  is  such 
as  to  render  their  ends  incandescent.  They  may  then  be  re- 
moved to  a  short  distance  without  interrupting  the  current, 
which  forces  its  way  through  the  air  and  produces  a  lumi- 
nous arc  of  great  intensity.  With  48  Bunsen's  elements,  the 
arc  is  about  one-fourth  of  an  inch  long.  The  light  is  of 


FIG.  222. 


264  ELEMENTS  OF  PHYSICS. 

far  greater  intensity  than  that  obtained  by  the  oxyhydro- 
gen  blow-pipe,  being  equal  to  that  of  572  wax  candles. 
With  600  elements,  the  arc  is  nearly  eight  inches  long,  and 
may  be  said  to  rival  the  brilliancy  of  the  sun. 

The  light  is  not  due  to  combustion,  but  to  the  transfer- 
ence of  the  intensely  heated  particles  of  carbon  from  the 
positive  to  the  negative  electrode.  In  consequence  of  this, 
the  positive  electrode  gradually  wears  away  and  the  negative 
electrode  receives  a  deposit.  The  effect  of  this  is  to  increase 
the  distance  between  the  electrodes;  and,  hence,  some  ar- 
rangement is  necessary  to  bring  them  together  in  proportion 
as  the  distance  alters.  This  may  be  done  by  the  hand,  or 
more  conveniently  by  clock-work. 

The  electric  light  is  admirably  adapted  for  illumination  in 
theaters  and  lecture-rooms,  but  is  not  well  adapted  for  gen- 
eral purposes  of  illumination.  Besides  the  cost  of  its  pro- 
duction and  the  skill  required  in  its  management,  the  very 
intensity  of  the  light  is  a  source  of  difficulty,  as  it  acts  inju- 
riously on  the  eye  and  throws  shadows  into  too  strong  relief. 

The  most  refractory  substances,  as  platinum,  quartz,  and 
lime,  when  introduced  into  the  arc  are  fused.  The  color  of 
the  light  varies  with  the  substances  placed  between  the 
terminals.  Gold  emits  a  bluish  light ;  silver,  an  emerald- 
green  ;  lead,  a  purple,  etc. 

408.  Chemical  effects.  If  a  chemical  compound,  in  a 
liquid  state,  be  made  to  form  a  part  of  the  external  voltaic 
circuit,  a  series  of  decompositions  will  take  place  like  those 
already  described  as  occurring  within  the  simple  voltaic 
element.  This  process  is  called  electrolysis. 

Fig.  223  represents  a  convenient  apparatus  to  show  the 
decomposition  of  water.  It  consists  of  a  glass  vessel,  through 
the  bottom  of  which  are  passed  two  wires  terminating  in 
platinum  electrodes.  The  vessel  being  filled  with  acidulated 


ELECTROLYSIS. 


265 


H 


FIG.  223. 


water,  two  glass  tubes  also  filled  with  water  are  inverted 
over  the  electrodes,  and  the  outer  wires  are  connected  with 
a  battery.  Five  of  Grove's  elements  will  cause  a  rapid 
decomposition  of  the  water ;  bub- 
bles of  gas  will  collect  in  the 
tube  above  each  pole.  Hydro- 
gen rises  from  the  negative  pole 
and  oxygen  from  the  positive. 
The  volume  of  the  hydrogen  lib- 
erated is  double  that  of  the 
oxygen. 

As  the  gases  evolved  are  in 
proportion  to  the  amount  of 
zinc  consumed,  a  modification 
of  this  apparatus,  called  a  vol- 
tameter, is  used  to  measure  the 
strength  of  a  battery. 

409.  The  decompositions  of  other  compounds   may 
be  effected   by  a  similar  apparatus.     If  the  electrodes  are 
plunged  in  solutions  of  binary  compounds,  like  chloride  of 
copper,  iodide  of  potassium,  cyanide  of  silver,  the   metals 
collect  at  the  negative  pole  and  the  non-metals  at  the  posi- 
tive.     On    the    principle   that  bodies   dissimilarly  charged 
attract  each   other,    the    metals    are   called    electro-positive 
substances  and  the  non-metals  electro-negative. 

410.  Ternary  salts  are  also  decomposed  by  the  current, 
the  metal  going  to  the  negative  pole,  and  the  acid,  on  the 
body  which    is    chemically  equivalent    to   it,  going    to    the 
positive. 

Ordinarily,  a  single  voltaic  element  will  suffice  for  the 
decomposition  of  a  salt.  The  condition  in  which  the  metal 
is  deposited  on  the  negative  electrode,  depends  somewhat  on 

the  strength  of  the  current.     When   the  action  is   rapid, 
PHYS.  23. 


266 


ELEMENTS  OF  PHYSICS. 


most  metals  are  deposited  as  loose,  flocculent  powders ;  but 
if  it  is  slow,  copper,  silver,  gold,  and  some  others  are  de- 
posited in  firm,  coherent  layers,  which  exactly  fit  the  surface 
of  the  electrode. 

411.  Electro  -  metallurgy  is  the  art  of  depositing  the 
metals  from  solutions  of  their  salts  by  means  of  the  electric 
current.  The  solution  is  decomposed  in  the  manner  just 
described,  and  the  pure  metal  is  deposited  on  the  negative 
electrode.  This  may  consist  of  any  article  whatever  that 


FIG.  224. 
If  the  material  is  non-conduct- 


has  a  conducting  surface, 
ing,  the  surface  may  be  rendered  conducting  by  covering  it 
with  finely  powered  graphite.  The  positive  electrode,  C, 
Fig.  224,  should  be  a  plate  of  the  same  metal  as  that  to  be 
deposited — in  order  that  the  acid  which  is  liberated  may 
dissolve  it,  and  thus  maintain  the  strength  of  the  solution. 
412.  The  processes  of  electro-metallurgy  may  be  ar- 
ranged in  two  divisions :  (1)  those  in  which  the  deposit 
remains  permanently  fixed  on  the  electrode,  and  (2)  those 
in  which  the  deposit  is  intended  to  be  removed.  The  first 
may  be  represented  by  electroplating  and  the  second  by 
eledrotyping. 


ELECTROTYPING. 


267 


The  apparatus  employed  in  electroplating  is  represented 
in  Fig.  224.  The  bath  consists  of  a  weak  solution  of  cya- 
nide of  silver.  The  articles  to  be  silvered  are  first  carefully 
cleaned,  then  attached  to  the  negative  pole  of  the  battery 
and  immersed  in  the  bath.  A  coating  of  pure  silver  begins 
to  form  at  once,  and  may  be  obtained  of  any  thickness 
desired.  When  the  articles  are  first  taken  from  the  bath, 
their  surfaces  appear  dull  and  white.  The  metallic  luster 
of  silver  is  then  communicated  to  them  by  burnishing. 

By  a  similar  process  articles  may  be  electro-gilded,  01 
coated  with  other  metals,  as  copper  and  nickel. 

413.  In  electrotyping,  it  is  usual  (1)  to  form  a  mold 
of  the  object  to  be  copied,  and  then  (2)  to  deposit  within 
this  a  coating  of  some  metal  sufficiently  thick  to  be  stripped 
off  whole.  Thus,  suppose  we  desire  to  copy  a  medal  in  cop- 
per. The  medal  is  first  rubbed  over  with  graphite  and  the 
excess  of  graphite  blown  off;  (2)  an  impression  of  the 
medal  is  taken  in  wax  and  the  wav:  coated  with  graphite, 
as  before ;  (3)  a  copper  wire  is  now  thrust  through  the  wax 
and  made  to  connect  with  the  layer  of  graphite;  finally, 
(4),  the  wax  mold  is  made 
the  negative  electrode  in  a 
bath  of  sulphate  of  copper. 
A  tough  coat  of  copper  will 
gradually  be  deposited  on 
the  surface  of  the  graphite, 
and,  after  a  day  or  two,  will 
be  sufficiently  thick  to  be 
removed.  The  plates  from 
which  this  book  was  printed  FlG.  225. 

wrere  electrotyped  in  this  \vay. 

The  student  may  easily  copy  small  articles  like  coins  and 
seals  by  the  simple  means  shown  in  Fig.  225.  A  is  a  glass 


268  ELEMENTS  OF  PHYSICS. 

vessel  containing  a  saturated  solution  of  sulphate  of  cop- 
per. B  is  a  lamp-chimney  closed  below  with  a  piece  of 
bladder,  and  containing  very  dilute  sulphuric  acid.  The 
apparatus  is  completed  by  putting  a  roll  of  amalga- 
mated zinc  in  the  sulphuric  acid,  and  connecting  it  by  a 
wire  to  the  object  to  be  copied  which  is  laid  below  the 
bladder.  The  connecting  wire  and  any  part  of  the  object 
which  it  is  not  desired  to  copy  must  be  carefully  coated 
with  wax  or  a  resin  varnish. 


KECAPITULATION. 


The  effects  of  the  current  within  its  path  are: 

1.  Physiological        .        .        .  Applied  in  some  diseases. 

2.  Calorific       ....  Applied  in  firing  mines. 

3.  Luminous    ....  Applied  in  the  electric  light. 

4.  Chemical      ....  Applied  in  electro-metallurgy. 


PHENOMENA  EXTERNAL  TO  THE  PATH  OF  THE  CURRENT. 

414.  The  voltaic  current  also  acts  inductively  upon 
conductors  external  to  its  path,  and  thereby  causes  phenom- 
ena which  closely  ally  its  action  to  magnetism.  These 
phenomena  may  be  grouped  in  two  divisions : 

1.  Electro-magnetism  considers   the   phenomena    in   which 
magnetic  attraction  and  repulsion  are  caused  by  the  voltaic 
current. 

2.  Electro-dynamic  induction  considers  the   production  of 
other  currents  in  the  vicinity  of  closed  circuits. 


ELECTRO -MAGNETISM. 


269 


Conversely,  permanent  magnets  act  inductively  on  con- 
ducting wires,  and  thereby  give  rise  to  electrical  currents 
without  the  aid  of  a  battery. 

(3)  Magneto -electricity  considers  the  production  of  elec- 
trical currents  by  means  of  permanent  magnets. 

ELECTRO-MAGNETISM. 


415.  Oersted  discovered,  in  1819,  that  a  magnetic  needle 
held  in  the  vicinity  of  a  voltaic  current  tends  to  place  itself 
at  right  angles  to  the  conducting  wire. 


FIG.  226. 

To  repeat  his  experiment,  a  magnetic  needle  is  allowed  to 
assume  its  natural  position,  pointing  north  and  south.  If, 
now,  the  wire  conducting  a  voltaic  current  be  held  parallel 
to  the  needle,  the  needle  will  be  deflected.  Fig.  226. 

The  direction  in  which  the  needle  should  turn  may  be 
remembered  by  the  following  rule :  Suppose  a  diminutive 
figure  of  a  man  to  be  so  placed  in  the  circuit  that  the  current 
shall  enter  by  his  feet  and  leave  by  his  head:  then  if  his  face  be 
turned  toward  the  needle,  its  north  pole  will  be  deflected  toward 
his  left. 

In  accordance  with  this  rule,  if  the  current  passes  above 


270 


ELEMENTS  OF  PHYSICS. 


the  needle  and  goes  from  south  to  north,  the  north  pole  of 
the  needle  will  turn  toward  the  west.  It  will  also  turn 
westward,  if  the  current  passes  below  the  needle  from  north 
to  south.  Hence,  if  the  wires  NS,  N'S'  be  joined  so  that 
the  current  shall-  pass  around  the  needle,  the  deflecting 


FIG.  227. 

power  will  be  doubled.  By  coiling  insulated  wire  many 
times  around  the  needle  the  deflecting  power  is  so  increased 
that  it  may  be  used  to  detect  the  presence  of  very  weak 
currents,  to  determine  their  direction,  and  even  to  measure 
their  intensity.  An  instrument  constructed  on  this  principle 
is  called  a  galvanometer. 

The  Astatic  galvanometer,  represented  in  Fig.  227,  derives 
its  name  from  the  fact  that  it  employs  two  magnetic 
needles  fastened  to  the  same  axis  of  suspension,  but  with 


FLOATING  BATTERY. 


271 


their  poles  reversed.  The  directive  force  of  the  earth  on 
the  needles  is  nearly  or  quite  neutralized. 

416.  If   the   conducting  wire    be    movable,  we   may 

obtain  results  the  converse  of  the  preceding;  that  is,  a 
straight  conducting  wire  will  tend  to  place  itself  at  right 
angles  to  a  magnet  held  in  its  vicinity. 

De  La  Rive's  floating  battery  (Fig.  228)  enables  us  to 
verify  this  fact.  It  consists  of  a  small  voltaic  element  which 
is  floated  in  acidulated  water  by  means  of  a 
cork.  The  conducting  wire  may  be  made 
straight  or  coiled.  The  spiral  coil  shown  in 
the  figure  is  called  a  Mix.  An  elongated 
helix  with  its  conducting  wire  returned 
through  the  axis  of  the  coil  is  a  solenoid. 
Fig.  229. 

417.  When  the   current  is   passing 

through  the  wire  it  exhibits  all  the  properties  of  a  magnet. 

1.    If  a  permanent  magnet  is  held  near  the  floating  helix, 


FlG.  229. 


one  face  of  the  coil  will  be  attracted  by  the  north  pole  of 
the  magnet  and  the  other  repelled. 

2.   Each  side  of  the  helix  will  attract  iron  filings. 


272 


ELEMENTS  OF  PHYSICS. 


3.  The  axis  of  the  helix  will  point  north  and  south. 

4.  If  two  solenoids  (Fig.  229)  are  brought  near  each  other, 
their  similar  ends  will  repel  each  other ;  their  dissimilar  ends 
will  attract  each  other. 

5.  If  the  conducting  wire  of  a  floating  battery  be  straight, 
and  a  wire  from  another  circuit  be  placed  parallel  to  it — 
(1)   The  wires  will  be  mutually  attracted  if  the  currents  pass  in 
the  same  direction,  but  (2)  will  be  repelled  if  the  currents  pass  in 
opposite  directions. 

418.   The  voltaic  current  may  also  induce  magnetism  in 

magnetic  substances.     If  a  bar  of  soft  iron,  NS,  be  placed 

in  the  axis  of  a  helix,  the  bar  will   ~ 

be   instantly  magnetized  on   closing 

the  circuit.     Fig.  230.     If  the  helix 

is  held  vertically  the  bar  will  not  fall 

out.     If  the  bar  be  pulled  down  a 

little  way  and  then  let  go,   it  will 

spring  back  to  its  former  position.     It  will  also  attract  bits 

of  iron  to  itself,  and  act  in  every  respect  like  a  magnet. 

When  the  circuit  is  broken  it  loses  its  magnetism  almost 

instantly. 

A  pleasing  modification  of  the  same  experiment  may  be 

had  by  passing  the  ends  of  two  semicircular  pieces  of  soft 
iron  within  a  helix,  as  shown  in  Fig. 
231.  On  closing  the  circuit,  they  will 
adhere  with  considerable  force. 


FIG.  230. 


FIG.  231. 


419.  Electro-magnets  are  bars  of 
soft  iron  which  become  magnets  under 
the  influence  of  the  voltaic  current.  Electro-magnets  of 
surprising  power  have  been  made  by  bending  bars  of  soft 
iron  in  the  form  of  a  horse-shoe,  and  surrounding  each  leg 
with  many  turns  of  insulated  copper  wire.  Fig.  232. 


PERMANENT  MAGNETS.  273 

When  a  strong  current  is  passing,  the  magnetism  induced 
is  far  greater  than  is  possible  in  a  permanent  magnet. 
Electro -magnets  have  been  made 
that  were  capable  of  sustaining 
nearly  two  tons. 

Permanent  magnets.  When  the 
current  is  broken,  the  magnetism  - 
ceases  instantly  if  the  iron  is  quite 
pure ;  but,  otherwise,  traces  of  the 
magnetism  will  remain  for  some 
time.  A  steel  bar  placed  in  the  FIG.  232. 

helix  (Fig.  230)  will  become  permanently  magnetized. 

420.  An  excellent  method  of  making  permanent  mag- 
nets is  shown  in  Fig.  233.     The  steel  horse-shoe  is  applied 
to  an  electro-magnet  and  a  piece  of  soft  iron   is  drawn  in 

the  direction  of  the  arrow 
beyond  the  curve,  and  is 
then  replaced  and  the  proc- 
ess frequently  repeated. 
Both  magnets  are  then 

turned  over  without   separating  them,  and  the  other  side 

treated  in  the  same  way. 

421.  Various  machines  have  been  devised  in  the  hope 
of  employing  the  prodigious  force  of  electro-magnets.     The 
electric  telegraph  is   by  far  the  most  important  application 
of  electricity.      Every  electric  telegraph  consists  essentially 
of  four  parts  :   (1)  a  voltaic  battery  for  generating  a  current ; 
(2)  a  circuit  consisting  of  an  insulated  metallic  connection 
between  two  places ;    (3)  a  key,  which  is  an  instrument  for 
sending   signals   from   one   station ;    (4)    an  instrument  for 
receiving  signals  at  the  other  station. 

1.    Any  constant  battery  may  be  used  for  generating  elec- 


274  ELEMENTS  OF  PHYSICS. 

tricity.  In  this  country,  some  modification  of  Daniell's  bat- 
tery is  generally  used. 

2.  The  two  stations  must  be  connected  by  at  least  one 
insulated  wire.  Generally  this  is  done  by  passing  galvanized 
iron  wire  over  glass  insulators  attached  to  a  series  of  tall 
wooden  posts. 

At  the  station  which  sends  the  dispatch,  the  line  is  con- 
nected with  the  positive  pole  of  the  battery,  but  as  the  cur- 
rent will  not  pass  unless  the  two  poles  of  the  battery  are 
connected,  it  is  also  necessary  to  have  a  second  conductor 
returning  in  the  opposite  direction  to  the  negative  pole  of 
the  battery. 

In  1837,  Stein heil  discovered  that  the  earth  might  be 
used  for  the  return  conductor.  To  effect  this,  large  metallic 
plates  are  buried  in  the  ground  at  each  station,  and  are 
connected  at  the  sending  station  with  the  negative  pole  of 
the  battery  and  at  the  receiving  station  with  the  line  wire. 
The  earth  really  dissipates  the  electricity,  but  the  effect  is 
the  same  as  if  it  were  an  infinitely  large  return  conductor 
offering  an  infinitely  small  resistance. 

422.  Morse's  telegraph,  which  is  more  extensively  used 
than  any  other,  requires  at  least  two  distinct  parts,  the  signal 
key  and  the  receiver.  Beside  these,  a  third  part,  called  a 
relay,  is  necessary  on  long  circuits  as  adjunct  to  the  receiver. 
These  parts  are  all  shown  in  Fig.  236.  If  messages  are  to 
be  received  and  answered,  each  station  will  require  a  full 
set  of  apparatus. 

The  signal  key  is  used  for  breaking  and  closing  the  circuit 
at  the  transmitting  station.  It  usually  consists  of  a  brass 
lever,  ad,  which  works  on  an  axis,  K,  supported  on  an  insu- 
lated base.  The  middle  of  the  lever  is  always  in  connection 
with  the  line  wire.  At  the  ends  are  two  metallic  points  by 
which  the  line  wire  may  be  brought  in  connection  either 
with  the  receiver  or  with  the  positive  pole  of  a  battery. 


MORSE'S  TELEGRAPH.  275 

(1)  When  the  lever  is  left  to  itself,  a  spring,  n,  forces 
the  end,  a,  down,  so  that  a  receiver  at  R'  (not  drawn  in  the 
figure)  is  in  condition  to  receive  a  dispatch  from  a  distant 
station.  (2)  When  a  dispatch  is  to  be  sent,  the  end,  d,  is 
depressed  by  applying  the  finger  to  an  ebonite  button,  /. 
The  current  passes  from  the  battery  up  the  point  d,  through 
the  lever  to  K,  along  the  wire  to  the  receiving  instrument, 
or  relay,  at  the  distant  station,  and  thence  returns  by  the 
earth,  making  the  circuit  complete.  When  the  finger  is 
removed,  the  current  ceases,  and  hence  the  operator  can 
close  the  circuit  for  a  longer  or  shorter  time,  at  his  pleasure, 
by  depressing  or  elevating  the  point  d. 

423.  The  receiver,  Fig.  234,  consists  (1)  of  an  electro- 
magnet whose  helices  form  part  of  the  line  circuit,  and  (2) 


FIG.  234. 

a  lever  which  is  worked  by  the  joint  action  of  the  electro- 
magnet and  an  adjustable  spring,  S. 

One  end  of  the  coil,  L,  is  connected  with  the  line  wire 
from  the  sending  station,  and  the  other,  E,  with  the  earth. 
When  the  circuit  is  closed,  the  electro-magnet  draws  down 
the  armature  A,  which  is  so  attached  to  a  horizontal  lever 
that  when  the  end  A  is  depressed,  the  other  end,  P,  is 


276  ELEMENTS  OF  PHYSICS. 

forced  up.  This  end  carries  a  steel  point,  or  style,  which 
writes  the  signals. 

For  this  purpose,  a  narrow  slip  of  paper  is  drawn  by 
clock-work  between  the  style  and  a  revolving  cylinder,  and 
is  indented  by  the  pressure  of  the  style.  When  the  circuit 
is  broken,  the  style  is  pulled  down  by  the  spring,  and  the 
paper  is  left  blank.  Hence,  by  varying  the  time  of  contact 
at  the  sending  station,  a  series  of  signals  consisting  of  dots 
and  lines  is  produced  at  the  receiving  station. 

The  following  is  the  modified  Morse's  alphabet : 


a  b  c  d        e         f  g  h         i         j 

k  I  m  n          o  p  q  r  s         t 

u  v  w  x  y  z  &  12 


34567  89  0 

_._        _._  __          _„_  _____ 

FIG.  235. 

424.  The  clicking  sound  of  the  armature  and  the  style 
indicates  to  the  ear  the  same  distinction  of  long  and  short 
signals  that  are  indicated  to  the  eye  upon  the  paper.  A 
skillful  operator  seldom  looks  at  the  paper  when  he  is  receiv- 
ing a  message.  In  most  cases,  the  paper  and  clock-work 
are  dispensed  with,  and  the  dispatch  is  read  only  by  sound. 

The  relay.  The  intensity  of  the  current  is  so  weakened 
after  it  has  traversed  a  few  miles,  that  the  recording  instru- 
ment can  be  worked  directly  by  the  line  current  only  on 
short  circuits.  In  circuits  exceeding  fifty  miles,  the  actual 
receiving  instrument  is  the  relay.  This  is  simply  an  electro- 
magnet whose  only  duty  is  to  open  and  close  a  local  circuit 
in  which  the  recording  instrument  is  included. 

The  manner  in  which  this  is  done  will  be  rendered  evi- 
dent by  an  inspection  of  Fig.  236.  The  line  current  passes 


THE  RELAY. 


277 


from  the  positive  pole  of  the  battery,  B,  through  the  key 
and  the  line  wire  to  the  relay,  thence  around  the  helices  of 
the  relay  and  down  to  the  earth  plate,  X.  The  earth  con- 
nection is  then  said  to  return  the  current  to  the  ground 
plate,  X',  and  thus  finally  completes  the  circuit  to  the 
negative  pole  of  the  battery. 

Each  time  the  line  current  passes  into  the  relay,  the 
electro-magnet  attracts  its  armature,  A,  which  is  fixed  at 
the  bottom  of  a  vertical  lever,  L.  At  the  same  moment, 
the  upper  end  of  the  lever  strikes  against  the  screw,  P. 
At  this  instant,  a  current  from  a  local  battery,  B',  enters  at 


Earth    Circuit  -« — 

FIG.  236. 

the  axis  of  the  lever,  ascends  to  the  screw,  P',  thence  passes 
to  the  electro -magnet  of  the  recording  instrument,  and 
finally  returns  to  the  local  battery  from  which  it  started. 
When  the  line  current  ceases,  the  lever  is  drawn  back  by 
the  spring  $',  and  the  local  circuit  is  broken.  By  this 
means,  the  local  current  is  made  to  act  in  unison  with  the 
line  current,  and  may  be  used  either  to  print  a  legible  dis- 
patch or  to  transmit  a  fresh  current  to  a  station  further  on. 

425.    The  electrical  fire-alarms,  now  extensively  used 
in  large  cities  for  indicating  the  localities  of  fires,  are  modi- 


278  ELEMENTS  OF  PHYSICS. 

fications  of  the  Morse  instrument.  The  properties  of  th0 
electro-magnet  have  also  been  practically  applied  to  variou? 
purposes.  Among  these  are  electric  pendulums,  electric 
clocks,  and  chronographs.  The  chronograph  is  an  instru- 
ment for  recording  the  time  at  which  any  phenomenon 
occurs.  Several  forms  of  this  instrument  have  been  devised 
which  have  been  used  to  register  automatically  the  fluctua- 
tions of  barometers,  thermometers,  and  the  winds. 

426.  Hitherto  the  attempts  to  use  the   electro-magnet 
as  a  motive    power   have    not   been    altogether    successful. 
Nevertheless,   small   electro-magnetic    machines   have    been 
employed  in  cases  where  economy  is  of  less  consequence  than 
convenience  and  facility  of  application,  as  in  running  sew- 
ing machines.     We  can  not  hope  that  they  will  ever  be  able 
to  compete  with  steam-engines  in  point  of  economy. 

427.  There   are  various  other  forms  of  the  telegraph, 
among  which  Wheatstone's    needle    telegraph    is    the    most 
important.     Its  receiving  instrument  consists  essentially  of  a 
delicate  galvanometer.      A  modification   of  this  instrument 
is  used  with  the  Atlantic  submarine  cable. 

CURRENT  INDUCTION. 

428.  The  phenomena  of  electro  -  dynamic  induction 
may  be  shown  by  the   apparatus   represented  in  Fig.  237. 
Let  P  be  a  helix  of  insulated  wire  through  which  a  primary 
current  is  passing  from  the  battery ;    and  I  a  second  helix 
connected  with  the  galvanometer.     When  the  primary  cur- 
rent is  brought  near  J,  a  secondary  or  induced  current  will  be 
set  up  in  I  and  will  cause  the  deflection  of  the  needle  in 
the  galvanometer. 

If  the  two  helices  are  kept  in  the  same  relative  position, 
the  induced  current  soon  ceases,  and  the  needle  returns  to 
its  old  position.  It  will,  however,  be  again  set  in  motion  if 


CURRENT  INDUCTION. 


279 


the  primary  current  is  in  any  way  changed ;  that  is,  if  the 
coil  be  removed,  or  if  the  current  be  broken  or  increased 
in  strength. 

An  induced  current  is,  therefore,  but  momentary  in  its 


FIG.  237. 

action ;    but,  nevertheless,  it  has  all  the  properties  of  the 
primary  current.      For  instance,  it  may  induce   other  CUP- 


FIG.  238. 

rents  on  adjacent  circuits,  and  give  rise  to  induced  currents 
of  the  third,  fourth,  and  even  the  seventh,  order. 


280  ELEMENTS  OF  PHYSICS. 

429.  Magneto-electrical  induction  is  like  the  preced- 
ing, except  that  it  is  caused  by  a  permanent  magnet.     If 
in  Fig.  238  we  employ  a  permanent  magnet  instead  of  the 
primary  coil,  we  shall  obtain  almost  identical  effects.     This 
is  as  we  should  be  led  to  expect,  because  we  have  learned 
that  a  helix  during  the  passage  of  a  current  is  essentially  a 
magnet. 

430.  The  magneto  -  electrical  machine  is  constructed 
on  this  principle.     Fig.  239. 

This  consists  of  a  permanent  magnet,  AB,  in  front  of 


FIG.  239. 

which  two  helices  of  insulated  copper  wire  are  made  to 
revolve  on  an  axis,  /,  by  means  of  a  winch.  The  cores  of 
the  helices  are  made  of  two  pieces  of  soft  iron  joined  by 
an  armature,  it' .  The  same  wire  is  coiled  about  the  two 
cores,  but  in  different  directions,  in  order  that  the  currents 
induced  by  the  opposite  magnetic  poles  should  be  in  the 
same  direction.  The  two  ends  of  the  wire  terminate  in 
two  metallic  plates  insulated  from  the  axis  and  from  each 
other  by  ivory,  and  are  alternately  connected  by  the  springs, 


INDUCTION  COILS.  281 

SSf.  On  turning  the  wheel,  a  current  of  electricity  is 
induced  in  the  coil  each  time  the  core  is  brought  before  the 
magnet.  It,  therefore,  gives  rise  to  a  rapid  succession  of 
momentary  currents. 

431.  This  instrument  is  capable  of  producing  sparks, 
decomposing    water,    igniting    wires,    and    other    effects   of 
dynamical   electricity.     If  a  break  piece,  not  shown  in  the 
figure,  be  added,  an  extra  current  of  great  tension  will  be 
produced.     If  the  handles,  PPf,  be  grasped  with  the  hands 
slightly   moistened,  the    muscles   contract   with  such   force 
that  they  no  longer  obey  the  will,  and  the  handles  can  not 
be  dropped.     From  its  convenience,  this  apparatus  is  gener- 
ally used   for  applying  the   effects  of  induced  currents  in 
therapeutical  operations. 

432.  Other  magneto  -  electrical  machines   have   been 
constructed   on   the  same  principle.     Some  of  these  are  of 
remarkable  power,  and  are  used  for  electroplating,  for  tele- 
graphing,  and   other    practical    applications    of   electricity. 
Wilde  has  constructed   a  machine  driven  by  steam  power 
which  yields  an  electric  light  of  surpassing  brilliancy,  and 
evolves  sufficient  heat  to  melt  iron  rods  fifteen  inches  long 
and  a  quarter  of  an  inch  thick. 

433.  Induction  coils  are  instruments  which  employ  both 
electric  and  magnetic  induction.      One  form  in  which  the 
helices  are  separable  is  shown  in  Fig.  240. 

The  primary  coil,  P,  of  coarse  insulated  copper  wire,  is 
connected  by  the  screw  cups  -j-  and  —  with  the  battery.  1 
is  the  secondary  coil  of  fine  insulated  copper  wire  to  which 
the  handles  are  attached.  M  is  a  bundle  of  iron  wires  which 
are  sufficiently  insulated  from  each  other  by  the  rust  which 
soon  gathers  on  them.  The  primary  current  is  made  to 

open  and   close  by  its  own  action.     This  is  effected  by  a 
PHYS.  24. 


282  ELEMENTS  OF  PHYSICS. 

small   electro-magnet,  B,  the  spring  of  whose   armature  is 
made  to  open  and  close  the  circuit. 

As  soon  as  the  coil  of  B  receives  the  current,  the  arma- 
ture is  drawn  down  and  the  circuit  is  broken.  This  re- 
leases the  armature  and  the  circuit  is  again  closed.  At 
every  interruption  of  the  primary  current  the  iron  wires 
become  magnetized  and  demagnetized,  and  act  inductively 
on  the  secondary  coil.  The  primary  current  also  acts  in- 
ductively on  the  secondary  coil,  and  by  this  joint  action  the 

M 


FIG.  240. 

intensity  of  the  induced  currents  become  much  increased, 
and  may  even  become  of  so  high  tension  as  to  produce  all 
the  effects  of  statical  electricity. 

434.  Ruhmkorflf's  coil  is  made  on  the  same  principle  as 
that  already  described.  The  utmost  care  is  taken  in  insu- 
lating the  wire  used.  The  secondary  helix  contains  from 
three  to  thirty  miles  of  fine  copper  wire.  With  three  Bun- 
sen's  elements  and  a  large  coil  the  induced  current  becomes 
of  amazing  intensity.  Some  of  the  effects  of  the  coil  are  as 
follows : 

1.    Physiological.    The   shocks   are   so   violent    as    to   be 


THERMO-ELECTRICITY.  283 

dangerous,  and   incautious   experimenters  have   been    pros- 
trated by  them. 

2.  Calorific.     Fine  iron  wires  brought  between  the  ends 
of  the  induced  wire  are  melted  and  vaporized. 

3.  Luminous.     Sparks  have  been  obtained  nineteen  inches 
in  length.     When  the  discharge  is  passed  into  rarefied  gases 
the  phenomena  of  auroral  light  is  produced  in  a  most  beau- 
tiful and  varied  manner.     These  experiments  are  performed 
in  sealed  glass  tubes,  known  as  Geisler's  tubes,  one  of  which 
is  shown  in  Fig.  241.     The  color  of  the  light  varies  with 


FIG.  241. 

the  vapor  inclosed  in  the  tube,  and  is  frequently  arranged 
in  bands  giving  the  appearance  of  stratified  light. 

4.  Mecfianieal     Plates  of  glass  over  an  inch  in  thickness 
may  be  pierced  by  the  discharge. 

5.  Leyden  jars  may  be  charged  and  discharged  by  means 
of   the    coil,    with    an    almost    continuous  spark    of   great 
brilliancy. 

THERMO-ELECTRICITY. 

435.  If  any  two  metals  are  soldered  together  and  heated 
at  their  junction,  an  electrical  current  is  evolved.  On  the 
other  hand,  if  their  junction  be  cooled,  an  electrical  current 
in  the  opposite  direction  will  be  produced.  These  currents 
are  called  thermo-electric  currents,  but  they  differ  in  no 
respect  from  those  already  studied. 


284  ELEMENTS  OF  PHYSICS. 

The  direction  of  the  current  within  the  pair  will  depend  on 
the  metals  which  are  associated  together.  The  following 
thermo-electric  series  is  so  arranged  that  if  any  two  of  the 
substances  named  are  soldered  together,  and  heated  at  the 
soldering,  the  current  will  pass  from  the  first  named  to  that 
succeeding  it. 

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The  most  efficient  electro-thermal  couple  is  said  to  be 
formed  of  artificial  sulphide  of 
copper  and  metallic  copper. 
Fig.  242.  The  usual  combina- 
tion is  bars  of  antimony  and 
bismuth.  Fig.  243  shows  a 
section  of  a  thermal  battery 
made  up  of  these  metals. 
The  greater  the  number  of  "  FIG.  242. 

pairs  the  greater  will  be  the  force  of  the 
current.  Although  the  electro-motive  force 
of  a  thermal  battery  is  always  low,  it 
may  be  used  to  obtain  the  same  results 
FIG.  243.  as  the  voltaic  battery. 

In  combining  the  bars,  it  is  necessary  to  join  both  ends 
of  all  the  bars  except  the  two  extremes.  Hence,  the  effect 
of  the  current  will  be  due  to  the  difference  of  temperature 
in  the  two  ends.  This  fact  is  utilized  in  the  thermo-multi- 
plier,  shown  at  T  in  Fig.  244.  It  consists  of  thirty  pairs 
of  bismuth  and  antimony,  inclosed  in  a  non-conducting 
frame,  and  connected  with  a  galvanometer  which  has  only 
a  few  turns  of  moderately  thick  wire.  The  slightest  differ- 


ANIMAL  ELECTRICITY. 


285 


ence  in   the  temperature   of  the  two  ends  of  the  thermo- 
multiplier  will  instantly  be  manifested  by  the  deflection  of 


FIG.  244. 

the  needle  of  the  galvanometer.     The  apparatus  is  used  in 
all  delicate  investigations   on   the  subject  of  radiant  heat. 

ANIMAL  ELECTRICITY. 

We  have  already  learned  that  electricity  produces  peculiar 
phenomena  in  living  animals,  and  that  one  of  the  most  sen- 
sitive galvanoscopes  may  be  had  in  the  legs  of  a  recently 
killed  frog.  Matteuci  has  reversed  this  last  experiment  and 
has  succeeded  in  evolving  a  current  by  means  of  a  battery 
formed  of  the  muscles  of  frogs. 

436.  Several  species  of  fish  have  the  power  of  giving, 
when  touched,  shocks  like  those  of  the  Leyden  jar.  Among 
these  are  the  torpedo,  the  gymnotus,  and  the  silurus.  Each 
of  these  fish  has  special  organs  for  the  production  of  elec- 
tricity. This  electrical  apparatus  is  under  the  control  of 
the  animal,  and  may  be  made  to  serve  as  a  means  of  offense 
and  defense. 


286  ELEMENTS  OF  PHYSICS. 


KECAPITULATION. 

The  science  of  electricity  includes  the  phenomena  of, 

1.  Electricity  that  may  be  insulated       .        .        .        Statical. 

2.  Electricity  continually  discharged  in  currents.       Dynamical. 

Dynamical  electricity  investigates  the  phenomena, 

I.  Within  the  path  of  the  current : 

1.  Due  to  chemical  action       ....          Galvanism. 

2.  Due  to  heat Thermo-Electricity. 

3.  Due  to  vital  action       ....    Animal  Electricity. 

4.  Due  to  magnetic  currents   ....          Magnetism. 

II.  External  to  the  path  of  the  current : 

1.  Inducing  magnetism  in  iron  and  steel  .  Electro-magnetism. 

2.  Inducing  currents  in  adjacent  circuits  .  Electro-dynamics. 

III.  Of  currents  induced  by  permanent 

magnets Magneto-electricity. 

Induced  currents  are  applied  : 

1.  For  physiological  and  therapeutical  purposes. 

2.  For  evolving  intense  light  and  heat. 

3.  For  effecting  chemical  changes. 

4.  For  making  permanent  and  temporary  magnets. 


THE   END. 


14  DAY  USE 

RETURN  TO  DESK  FROM  WHICH  BORROWED 

LOAN  DEPT. 

This  book  is  due  on  the  last  date  stamped  below,  or 

on  the  date  to  which  renewed. 
Renewed  books  are  subject  to  immediate  recall. 


JUN9-196637 


1  I 


RECEIVED  BY 


JUKI-    G82RCO       JUN  18  1385 


IRCULATION  DEPT* 


MAR  2  3  1977  8 


- — 


LD  21A-60m-10,'65 
(F7763slO)476B 


General  Library 

University  of  Californis 

Berkeley 


GENERAL  LIBRARY  -  U.C.  BERKELEY 


BDOQ77MEM8 


